Equation Calculator
Type an equation such as 2x + 3 = 11 or x² − 5x + 6 = 0 and get every solution, the steps and a graph — or solve a system of two or three linear equations.
- Solve for x
- 2 × 2 and 3 × 3 systems
- With steps
- Private
Use any single letter for the unknown. Powers: x^2 or x². Functions such as sqrt, ln, log and sin (in radians) work too.
Coefficients
Whole numbers, decimals or fractions such as 3/4. An empty box counts as 0.
Coefficients
Whole numbers, decimals or fractions such as 3/4. An empty box counts as 0.
Step by step
How to solve an equation
Write it as you would on paper.
- 1
Choose the type
One equation with one unknown, or a system of two or three linear equations.
- 2
Enter the equation
Type both sides with an equals sign, for example 3x − 7 = 11. For systems, fill in the coefficients.
- 3
Read the solutions
See every solution, how it was found and a graph showing where the two sides are equal.
From 2x + 3 = 11 to three unknowns
A solver for homework, exam revision and quick checks.
Any single-variable equation
Polynomials up to degree 8 are solved completely; other equations are solved numerically.
Real and complex roots
Quadratics and higher-degree equations show complex solutions such as 2 ± 3i as well.
Linear systems
Two equations in x and y or three in x, y and z, solved exactly with fractions.
Steps and check
Standard form, the formula used and a check by substituting the solution back in.
Graph
The curve of left side minus right side, with each real solution marked on the axis.
Link to your calculation
Copy a link that reopens the calculator with your numbers filled in — handy for sharing or saving a scenario.
Made for phones
Large fields, the right keyboard for numbers and a layout that fits small screens.
Private by design
Everything is calculated in your browser. Your numbers are not sent to a server.
How equations are solved
Solving an equation means finding the values of the unknown that make both sides equal. The basic technique is to do the same operation on both sides until the unknown stands alone: 2x + 3 = 11 becomes 2x = 8 after subtracting 3, and x = 4 after dividing by 2. Every linear equation has exactly one solution, unless the unknown cancels out — then there is either no solution or every number is one.
A quadratic equation ax² + bx + c = 0 has two solutions, given by x = (−b ± √(b² − 4ac)) ÷ 2a. They can be two different real numbers, one repeated number or a pair of complex numbers. In general a polynomial equation of degree n has exactly n solutions when complex and repeated ones are counted; from degree 5 upwards there is no general formula, so the roots are computed numerically.
A system of linear equations asks for values that satisfy several equations at once. Two equations in two unknowns describe two lines: they meet in one point (one solution), are parallel (no solution) or coincide (infinitely many). The calculator uses elimination with exact fractions, so results such as x = 7/3 are not rounded.
Types of equation and their solutions
| Type | Example | Solutions |
|---|---|---|
| Linear | 3x − 7 = 11 | x = 6 |
| Quadratic | x² − 5x + 6 = 0 | x = 2 and x = 3 |
| Cubic | x³ − 6x² + 11x − 6 = 0 | x = 1, 2 and 3 |
| Exponential | 2^x = 32 | x = 5 |
| Radical | sqrt(x + 5) = 4 | x = 11 |
| 2 × 2 system | 2x + 3y = 12, x − y = 1 | x = 3, y = 2 |
Tips
- For a quadratic with vertex, discriminant and factored form, use the Quadratic Calculator.
- Just need to evaluate an expression? The Scientific Calculator is quicker.
- Working with a proportion such as a : b = c : x? The Ratio Calculator solves it directly.
- Always check a solution by substituting it into the original equation — especially after squaring both sides, which can introduce false solutions.
Frequently asked questions
Can’t find your answer? Contact us — we reply quickly.
How do I solve a linear equation?
Collect the terms with x on one side and the numbers on the other, then divide by the coefficient of x. For 5x − 4 = 2x + 8: 3x = 12, so x = 4.
Which equations can this calculator solve?
Any equation with one unknown. Polynomial equations up to degree 8 are solved completely, including complex roots. Equations with roots, logarithms, exponentials or trigonometric functions are solved numerically between −100 and 100.
Can I use a letter other than x?
Yes. Any single letter works as the unknown, for example t or n. Use one unknown per equation; for several unknowns choose a system.
What does “no solution” mean?
The two sides can never be equal, as in x + 1 = x + 2. If instead both sides are always equal, as in 2(x + 1) = 2x + 2, every number is a solution.
How do I solve a system of equations?
Choose the 2 × 2 or 3 × 3 system and enter the coefficients of each equation. The calculator solves the system exactly with fractions and shows a check by substituting the solution.
Are my numbers stored or sent anywhere?
No. The calculation runs in your browser. Your last inputs are remembered on your own device only, so the form is still filled in when you come back; use Reset to clear them.
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