Equation Solver

Solve linear equations, quadratic equations, and systems of equations in seconds. Get exact solutions, discriminants, nature of roots, and step-by-step breakdown.

Choose Equation Type

How the Equation Solver Works

This tool automatically analyzes your input and applies the correct algebraic method: linear solving, quadratic formula, or Cramer's rule for systems of equations.

Formulas Used

1) Linear Equation: ax + b = 0

x = -b / a

2) Quadratic Equation: ax² + bx + c = 0

Discriminant: Δ = b² − 4ac

Roots:
x₁ = (−b + √Δ) / (2a)
x₂ = (−b − √Δ) / (2a)

3) System of Equations

a₁x + b₁y = c₁
a₂x + b₂y = c₂

Using Cramer's Rule:

D  = a₁b₂ − a₂b₁
Dx = c₁b₂ − c₂b₁
Dy = a₁c₂ − a₂c₁

x = Dx / D
y = Dy / D

Common Uses

Algebra homework & learning tools
Engineering and physics calculations
Business and financial model equations
Real-world problem solving

Frequently Asked Questions

You will get complex roots in the form a + bi and a − bi.

If the determinant D = 0 but Dx or Dy != 0, the system is inconsistent and has no solution.

Variables are symbolic. You can interpret x and y as any two unknowns.