What is the discriminant?

The discriminant (b² - 4ac) indicates the nature of roots. If >0, two distinct real roots exist. If =0, one real double root exists. If <0, two complex roots exist.

Quadratic Equation Solver

Solve quadratic equations and calculate roots and discriminants.

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Parameters

R Reset

Coefficient aFirst coefficient or term in the mathematical formula.

-10,00010,000

Coefficient bSecond coefficient or term in the mathematical formula.

-5

-10,00010,000

Coefficient cThird coefficient or term in the mathematical formula.

-10,00010,000

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Equation Roots

x = 3.0000, x = 2.0000

Discriminant1

x₁3.0000

x₂2.0000

Result Interpretation

The quadratic equation solution is x = 3.0000, x = 2.0000.

Mathematical Explanation

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

Quadratic equation solved. Roots: x = 3.0000, x = 2.0000

How to Use the Quadratic Equation Solver

Find the roots of any standard quadratic equation ax² + bx + c = 0.

Input variables:

Coefficient a: Bounded parameter in the mathematical model.
Coefficient b: Bounded parameter in the mathematical model.
Coefficient c: Bounded parameter in the mathematical model.

Quadratic Equation Solver: Roots, Parabolas, & Discriminants

Learn the quadratic formula, how the discriminant determines real or complex roots, and step-by-step parabola solving.

Read Full Guide →