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🧠 Algebra Calculator

Solve linear and quadratic equations step-by-step. Type directly or use the specialised keyboard.

2x + 3 = 7
Tips: use = for equations, ^ for powers — type x^2 and it becomes x². Multiplication is implicit — type 2x or 3(x+1).
2x + 3 = 7 x² − 5x + 6 = 0 2x² + 4x − 6 = 0 x³ − 6x² + 11x − 6 = 0 x³ − 3x + 1 = 0 x⁴ − 5x² + 4 = 0
Solution

About the Algebra Calculator

The Algebra Calculator solves one-variable linear and quadratic equations and shows the full working, step by step. Enter your equation using the on-screen keyboard — numbers, the variable x, operators, parentheses and powers (^) are all supported. Implicit multiplication is allowed, so you can type 2x, 3(x+1) or (x+2)(x−5). All calculations run entirely in your browser — nothing is sent to a server.

How to Solve a Linear Equation

  1. Simplify both sides. Expand any brackets and combine like terms.
  2. Move the variable to one side by adding or subtracting the same quantity from both sides.
  3. Move constants to the other side using the same inverse-operations principle.
  4. Divide both sides by the coefficient of x to isolate the variable.

For example, to solve 2x + 3 = 7: subtract 3 from both sides to get 2x = 4, then divide by 2 to get x = 2.

How to Solve a Quadratic Equation

A quadratic equation has the standard form ax² + bx + c = 0. Solve it with the quadratic formula:

x = (−b ± √(b² − 4ac)) / 2a

  • The discriminant Δ = b² − 4ac determines the nature of the roots.
  • If Δ > 0, the equation has two distinct real roots.
  • If Δ = 0, it has one repeated real root.
  • If Δ < 0, the roots are complex (a pair of conjugates of the form p ± qi).

Common Uses for an Algebra Calculator

  • GCSE, A-Level and Leaving Certificate homework and revision
  • Checking your own working when solving by hand
  • University-level problem sets in engineering, physics and economics
  • Testing the solutions of real-world word problems translated into equations
  • Exploring how coefficients change the solution set

Frequently Asked Questions

Can I use letters other than x? The calculator uses x as the variable. Substitute any letter you use in your problem for x before entering.

Does it handle fractions and decimals? Yes — enter fractions with the division operator (e.g. x/2) and decimals with a full stop (e.g. 0.5x).

Does it solve systems of equations? Not yet — this tool solves one equation in one variable. For simultaneous equations, solve one by substitution and use this calculator for the resulting single-variable equation.

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Important Note: This tool is intended to provide estimates and should not be used as a substitute for professional advice. Information generated by these calculators may be incomplete and does not account for all individual circumstances. Always seek the counsel of a certified expert (such as a financial advisor, healthcare provider, or licensed engineer) before taking action based on these results.

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