Equation Solver

Solve linear, quadratic, and polynomial equations with step-by-step solutions

Equation Input
Enter your equation and select the type

Use ^ for exponents (x^2) or write x² directly

Solution
Step-by-step solution and analysis

Enter an equation to see the step-by-step solution

Equation Examples
Click to load common equation types and examples

Simple Linear

Basic linear equation

2x + 5 = 11

Linear with Fractions

Linear with decimals

0.5x - 3 = 7

Simple Quadratic

Factorable quadratic

x^2 - 5x + 6 = 0

Quadratic Formula

Standard quadratic

x^2 + 2x - 3 = 0

Perfect Square

Repeated root

x^2 - 4x + 4 = 0

Complex Roots

Complex solutions

x^2 + x + 1 = 0

Equation Solving Methods

Linear Equations

Form: ax + b = c

Solved by isolating x: x = (c - b) / a. Always has exactly one solution unless a = 0 (no solution or infinite solutions).

Quadratic Equations

Form: ax² + bx + c = 0

Solved using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The discriminant determines the nature of solutions.

Discriminant Analysis

Δ = b² - 4ac

  • • Δ > 0: Two distinct real roots
  • • Δ = 0: One repeated real root
  • • Δ < 0: Two complex conjugate roots

Verification

Always check your solutions

Substitute each solution back into the original equation to verify that both sides are equal. This confirms the solution is correct.