Solve Linear & Quadratic Equations Instantly

Coefficient of x
Constant term

How to Use This Equation Solver

Follow these simple steps to solve equations quickly.

1

Select Equation Type

Choose between Linear (ax + b = 0) or Quadratic (ax² + bx + c = 0) equation.

2

Enter Coefficients

Input the coefficients for your equation. For linear: a and b. For quadratic: a, b, and c.

3

Solve

Click "Solve Equation" to get instant results with step-by-step solutions.

Equation Examples

📐

Simple Linear

Equation: 2x + 4 = 0
Solution: x = -2
📊

Quadratic (Two Solutions)

Equation: x² - 5x + 6 = 0
Solutions: x = 2, x = 3
🔢

Quadratic (One Solution)

Equation: x² - 4x + 4 = 0
Solution: x = 2 (double root)

Understanding Equations

Linear Equations (1st Degree)

A linear equation has the form: ax + b = 0

Solution: x = -b/a

Quadratic Equations (2nd Degree)

A quadratic equation has the form: ax² + bx + c = 0

x = (-b ± √(b² - 4ac)) / 2a

Discriminant (Δ = b² - 4ac):

  • Δ > 0: Two distinct real solutions
  • Δ = 0: One repeated real solution
  • Δ < 0: Two complex conjugate solutions

Frequently Asked Questions

What is a linear equation?

A linear equation is a first-degree polynomial equation with one variable. It has the form ax + b = 0, where a ≠ 0.

What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation with the form ax² + bx + c = 0, where a ≠ 0.

Can quadratic equations have complex solutions?

Yes! When the discriminant (b² - 4ac) is negative, the equation has two complex conjugate solutions.

What if coefficient a is zero?

If a = 0 in a quadratic equation, it becomes a linear equation. Our solver automatically handles this case.

Instant Solutions

Get equation solutions in milliseconds with our optimized algorithm.

Step-by-Step

View detailed solution steps to understand the solving process.

Complex Numbers

Handles real and complex solutions for quadratic equations.