Algebra Calculator

Solving for x Without the Scratch Paper

Linear equations, quadratic equations, and algebraic expressions all follow different solution paths, but they share the same starting frustration: one misplaced sign and the whole answer is wrong. This calculator uses a symbolic math engine to parse an equation or expression exactly as written — including implicit multiplication like 2x instead of requiring 2*x — and solves it algebraically rather than by trial and error.

The Approach

Linear equation: rearrange to isolate x, then solve
Quadratic equation: set to ax² + bx + c = 0, then solve for all roots
Simplify expression: combine like terms into reduced form

For equations containing an equals sign, the calculator moves everything to one side (left-hand side minus right-hand side) before solving, so 2x + 3 = 7 and 2x + 3 - 7 = 0 are handled identically.

Where Symbolic Algebra Comes Up

Homework verification — checking a worked solution to a linear or quadratic equation before submitting it.
Simplifying messy expressions — collapsing an expression like 2x + 3x - 5 + 2 down to its simplest form before using it elsewhere.
Quick root-finding — getting exact roots of a quadratic without manually applying the quadratic formula each time.

Example inputs and what each mode returns
Mode	Input	Result
Linear Equation	2x + 3 = 7	x = 2
Quadratic Equation	x^2 - 5x + 6 = 0	x = 2, 3
Simplify Expression	2x + 3x - 5 + 2	5x - 3

How to Use This Calculator

Choose a mode: Solve Linear Equation, Solve Quadratic Equation, or Simplify Expression.
Type the equation (e.g. 2x + 3 = 7) or expression (e.g. 2x + 3x - 5 + 2) into the input field.
Select Calculate to see the step-by-step explanation and the final result.

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Need the discriminant and both roots broken out explicitly? The Quadratic Equation Calculator shows that work directly, and Geometry Calculator covers area, perimeter, and volume formulas.