Equation Solver

Solve linear and quadratic equations step by step

Equation Solver

Equation Type*

Choose linear or quadratic equation

Coefficient a*

Coefficient of x² (quadratic) or x (linear)

Coefficient b*

Coefficient of x (quadratic) or constant (linear)

Coefficient c*

Constant term (quadratic only)

How to Use

Select whether you want to solve a linear (ax + b = 0) or quadratic (ax² + bx + c = 0) equation. Enter the coefficients a, b, and c, then click Calculate. The solver will find all solutions, including complex roots for quadratic equations.

Formula

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Examples

x² − 5x + 6 = 0

Using the quadratic formula: discriminant = 25 - 24 = 1. Solutions: x₁ = 3, x₂ = 2.

2x² + 4x + 2 = 0

Discriminant = 16 - 16 = 0. One repeated root: x = -1.

3x − 9 = 0

Linear equation: x = 9/3 = 3.

Frequently Asked Questions

What is the quadratic formula?▾

The quadratic formula is x = (-b ± √(b²-4ac)) / 2a. It gives the solutions for any quadratic equation ax² + bx + c = 0.

What does the discriminant tell you?▾

The discriminant (b²-4ac) indicates the nature of roots: positive = two real roots, zero = one repeated root, negative = two complex roots.

Can this solve cubic or higher-degree equations?▾

Currently this calculator handles linear and quadratic equations. Cubic and higher-degree equations require more advanced methods.

Equation Solver

Solve linear and quadratic equations step by step

Equation Solver

Equation Type*

Choose linear or quadratic equation

Coefficient a*

Coefficient of x² (quadratic) or x (linear)

Coefficient b*

Coefficient of x (quadratic) or constant (linear)

Coefficient c*

Constant term (quadratic only)

How to Use

Formula

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Examples

x² − 5x + 6 = 0

Using the quadratic formula: discriminant = 25 - 24 = 1. Solutions: x₁ = 3, x₂ = 2.

2x² + 4x + 2 = 0

Discriminant = 16 - 16 = 0. One repeated root: x = -1.

3x − 9 = 0

Linear equation: x = 9/3 = 3.

Frequently Asked Questions

What is the quadratic formula?▾

The quadratic formula is x = (-b ± √(b²-4ac)) / 2a. It gives the solutions for any quadratic equation ax² + bx + c = 0.

What does the discriminant tell you?▾

The discriminant (b²-4ac) indicates the nature of roots: positive = two real roots, zero = one repeated root, negative = two complex roots.

Can this solve cubic or higher-degree equations?▾

Currently this calculator handles linear and quadratic equations. Cubic and higher-degree equations require more advanced methods.