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Calixo

Quadratic Equation Calculator

Solve ax² + bx + c = 0 for its real roots, instantly.

Inputs

Coefficient of x².

Coefficient of x.

Constant term.

Saved Scenarios

— select 2+ to compare

x₁

2.000

x₂

1.000

Discriminant

1.00

Spark says

How it's calculated

Formula

x=−b±b2−4ac2ax = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}
a, b, c
— Coefficients of ax² + bx + c = 0

What is the Quadratic Equation Calculator?

A quadratic equation has the form ax² + bx + c = 0. The quadratic formula solves it directly using the coefficients a, b and c.

How to use it

  1. 1 Enter the coefficient of x² (a).
  2. 2 Enter the coefficient of x (b).
  3. 3 Enter the constant term (c).

Worked examples

x² - 3x + 2 = 0

Roots are x = 2 and x = 1.

Try it

Limitations

  • •Only real roots are shown — when the discriminant is negative, the true roots are complex numbers.

Common mistakes

  • ⚠️ Entering a = 0, which makes the equation linear, not quadratic — division by zero will produce an invalid result.

Frequently asked questions

What does the discriminant tell you?

Its sign tells you how many real roots exist: positive means two, zero means one repeated root, and negative means none (only complex roots).