Quadratic Equation Solver

Solve ax² + bx + c = 0 and find real or complex roots

Solve an equation of the form ax² + bx + c = 0. Enter the three coefficients and you'll get the discriminant and the real (or complex) roots.

1x² + (-3)x + (2) = 0

Discriminant

1.0000

two real roots

Solutions

x₁ = 2.0000, x₂ = 1.0000

How to Use This Calculator

  1. Enter the coefficient a (the number in front of x²).
  2. Enter the coefficient b (the number in front of x).
  3. Enter the constant c.
  4. Read the discriminant and the roots.

Why Use This Calculator?

  • Checking algebra homework.
  • Finding where a parabola crosses the x-axis.
  • Solving a real-world problem that fits a quadratic shape, like projectile height.

Real-World Examples

x² − 5x + 6 = 0

Here a=1, b=−5, c=6. The roots are x = 2 and x = 3, since both make the equation true.

x² + 1 = 0

With a=1, b=0, c=1, the discriminant is negative (−4), so the roots are complex: ±i.

The quadratic formula

The roots come from x = (−b ± √(b² − 4ac)) ÷ (2a). The piece under the square root, b² − 4ac, is the discriminant. If it's positive you get two real roots, if it's zero you get one, and if it's negative the roots are complex.

Frequently Asked Questions

What does the discriminant tell me?

It predicts the type of answer: positive means two real roots, zero means one repeated root, and negative means two complex roots.

What if a is zero?

If a is zero, the equation isn't quadratic — it's a straight line. Enter a non-zero value for a to use this solver.

Can it show complex roots?

Yes. When the discriminant is negative, the roots are shown as complex numbers.

Important Disclaimer

Solves standard quadratic equations. Results are exact for the coefficients entered.

Privacy

Your coefficients stay in your browser and aren't stored or sent.

Related Calculators

Exponent Calculator

Calculate powers and exponents

Scientific Calculator

Advanced scientific calculations with trig, log, and more

Pythagorean Theorem Calculator

Solve for a missing side of a right triangle

Percentage Calculator

Calculate percentages, increases, and decreases

Fraction Calculator

Add, subtract, multiply, and divide fractions