The equation solver allows to solve equations with an unknown with calculation steps : linear equation, quadratic equation, logarithmic equation, differential equation.

equation_solver online

An **equation** is an algebraic equality involving one or more unknowns.
Solving an equation is the same as determining that unknown or unknowns.
The unknown is also called a variable.
This **equation calculator** can solve equations with an unknown,
the calculator can solve **equations with variables on both sides** and also **equations with parentheses**:

- Solving linear equation
- Solving quadratic equation
- Solving cubic equation
- Solving zero product equation
- Solving absolute value equation (equation with abs function)
- Solving exponential equation
- Solving logarithmic equation (equation involving logarithms)
- Solving trigonometric equation (equation involving cosine or sine)
- Solve online differential equation of first degree
- Solve online differential equation of the second degree

A **first-degree equation** is an equation of the form `ax=b`. This type of equation is also called a **linear equation**.
To solve these equations we use the following formula `x=b/a`.

**linear** **equation solving** of the form ax=b s is done very quickly,
when the variable is not ambiguous, just enter **equation** to **solve** and then click solve,
then the result is returned by **solver**.
Details of calculations that led to the resolution of the linear equation are also displayed.
To solve the linear equation following 3x+5=0, just type the expression
3x+5=0
in the calculation area, then click on "solve" button, result is returned `[x=-5/3]`.
it is also possible to **solve equations** the form of `(ax+c)/g(x)=0` or equations that may be in this form
, g(x) represents a function.
When you enter an expression without '=' sign; the function returns when possible values for which expression is zero.
For example, enter x+5 and resolve back to x+5=0 and solve.

The calculator can solve equations with variables on both sides like this: `3x+5=2x`, just enter 3x+5=2x to get the result.

The calculator can solve equations with parentheses like this: `6*(3x+5)=5*(2x+3)`, just enter 6*(3x+5)=5*(2x+3) to get the result.

- `(x-1)/(x^2-1)=0` returns the message no solution, domain definition is taken into account for the calculation, the numerator admits x = 1 as the root but the denominator is zero for x = 1 , 1 can't be a equation solution. The equation does not admit a solution.
- equation_solver(`1/(x+1)=3`) returns `[-2/3]`

A **second-degree equation** is an equation of the form `ax^2+bx+c=0`. This type of equation is also called a **quadratic equation**.
To solve these equations the
discriminant
is calculated with the following formula `Delta=b^2-4ac`.

The discriminant is a number that determines the number of solutions of an equation.

- When the discriminant is positive, the equation of the second degree admits two solutions, which are given by the formula `(-b-sqrt(Delta))/(2a)` and `(-b+sqrt(Delta))/(2a)`;
- When the discriminant is null, the quadratic equation admits only one solution, it is said to be a double root, which is given by the formula `(-b)/(2a)`;
- When the discriminant is negative, the polynomial equation of degree 2 admits no solution.

**Solve quadratic equation** **online** of the form has `ax^2+bx+c=0` is
very quickly, when the variable is not ambiguous, just enter the equation to solve and click on the calculation,
the result is returned. Steps of the calculations that led to the resolution of the quadratic equation are also displayed.
To solve the quadratic equation following `x^2+2x-3=0`, just type the expression
x^2+2x-3=0
in the calculation area, then click on calculate, the result is returned `[x=-3;x=1]`

To **solve an equation with variables on both sides of the equality using the calculator**, like this one `x^2+x=2x^2+4x+1`, just type the expression
x^2+x=2x^2+4x+1
in the calculation area, then click on calculate, the result is returned `[x=(-3+sqrt(5))/2;x=(-3-sqrt(5))/2]`

It is also possible to solve the equations of the form `(ax^2+bx+c)/g(x)=0` or equations that may be in this form,
g(x) represents a function.

- equation_solver(`1/(x+1)=1/3*x`) returns `[(-1+sqrt(13))/2;(-1-sqrt(13))/2]`
- `(x^2-1)/(x-1)=0` returns -1, the entire definition is taken into account for the calculation of the numerator admits two roots 1 and -1 but the denominator is zero for x = 1, 1 can not be the solution of equation.

The equation calculator **solves some cubic equations**. In cases where the equation admits an obvious solution,
the calculator is able to find the roots of a polynomial of the third degree.
So the calculator will have no problem solving a third degree equation like this: equation_solver(`-6+11*x-6*x^2+x^3=0`).

Again, the solutions of the cubic equation will be accompanied by explanations which made it possible to find the result.

The **zero product property** is used to solve equations of the form A*B=0 , that this equation is zero only if A = 0 or B = 0.
To **solve** this type of **equation** can be done if A and B are polynomials of degree less than or equal to 2.
The details of the calculations that led to the resolution of the equation is also displayed.
It is also possible to solve the equations of the form `A^n=0`, if A is a lower degree of polynomial or equal to 2.

- equation_solver(`(x+1)(x-4)(x+3)=0;x`) returns `[-1;4;-3]`
- `(x^2-1)(x+2)(x-3)=0` returns `[1;-1;-2;3]`.

The solver allows **to solve equation** involving the ** absolute value**
it is able to solve linear equations using absolute values,
quadratic equations involving absolute values but also other many types of equation
with absolute values.

Here are two examples of using the equation calculator to solve an equation with an absolute value:

- `abs(2*x+4)=3`, solver shows details of the calculation of an linear equation with absolute value.
- `abs(x^2-4)=4`, solver shows the calculation steps for solving an quadratic equation with absolute value.

The **equation calculator** allows **to solve equation** involving the **exponential**
it is able to solve linear equations using exponential,
quadratic equations involving exponential but also other many types of equation
with exponential.

Here are two examples of using the calculator to solve an equation with an exponential:

- `exp(2*x+4)=3`, solver shows details of the calculation of an linear equation with exponential.
- `exp(x^2-4)=4`, solver shows the calculation steps for solving an quadratic equation with exponential.

**Solve logarithmic equation** ie some equations involving logarithms is possible.
In addition to providing the result, the calculator provides detailed steps and calculations that led
to the resolution of the logarithmic equation.
To solve the following equation logarithmic ln(x)+ln(2x-1)=0,
just type the expression in the calculation area, then click on the calculate button.

The **equation calculator** allows to **solve circular equations**, it is able to
**solve an equation with a cosine**
of the form **cos(x)=a** or an **equation with a sine** of the form **sin(x)=a**.
Calculations to obtain the result are detailed, so it will be possible to solve equations like
`cos(x)=1/2`
or
`2*sin(x)=sqrt(2)`
with the calculation steps.

The function equation_solver can **solve first order linear differential equations online**,
to solve the following differential equation :
y'+y=0, you must enter equation_solver(`y'+y=0;x`).

The function equation_solver can **solve second order differential equation online**,
to solve the following differential equation :
y''-y=0, you must enter equation_solver(`y''-y=0;x`).

To practice the different calculation techniques, several quizzes on solving equations are proposed.

equation_solver(equation;variable), variable parameter may be omitted when there is no ambiguity.

- equation_solver(`3*x-9`) is equal to write equation_solver(`3*x-9=0;x`) the returned result is 3.
- equation_solver(`3*x+3=5*x+2`) returns `1/2`

- Solving the equation `2*x^2-2=x^2+x` with the function equation_solver(`2*x^2-2=x^2+x`) returns two solutions separated by a semicolon [x=-1;x=2]

- Solving the equation `-6+11*x-6*x^2+x^3=0` with the function equation_solver(`-6+11*x-6*x^2+x^3=0`) returns three solutions.

- equation_solver(`y'+y=0;x`) returns `[y=k*exp(-x)]` k represents a constant.
- equation_solver(`y''-y=0;x`) returns `[y=a*exp(-x)+b*exp(x)]` a and b are constants.

See also

- Solving quadratic equation with complex number : complexe_solve. The complex number equation calculator returns the complex values for which the quadratic equation is zero.
- Calculation of the discriminant online : discriminant. Calculator that allows the calculation of the discriminant of a quadratic equation online.
- Find equation of a straight line from two points : equation_straight_line. The equation straight line calculator allows to calculate the equation of a straight line from the coordinates of two points with step by step calculation.
- Find the equation of tangent line : equation_tangent_line. The tangent line equation calculator is used to calculate the equation of tangent line to a curve at a given abscissa point with stages calculation.
- Pythagorean theorem calculator : pythagorean. The calculator uses the Pythagorean theorem to verify that a triangle is right-angled or to find the length of one side of a right-angled triangle.
- Solve for x calculator : equation_solver. The equation solver allows to solve equations with an unknown with calculation steps : linear equation, quadratic equation, logarithmic equation, differential equation.
- Inequality calculator : inequality_solver. Inequality solver that solves an inequality with the details of the calculation: linear inequality, quadratic inequality.
- Solve system of linear equations : solve_equations. The solver of systems of linear equations allows to solve equations with several unknowns: system of equations with 2 unknowns, system of equations with 3 unknowns, system with n unknowns.
- Countdown solver : arithmetic_solver. This countdown solver allows finding a target number from a set of integer in using arithmetic operations.

Equations | Real functions