Solve quadratic equations of the form ax² + bx + c = 0. This tool supports real and complex solutions with step-by-step explanation.
Enter coefficients

Discriminant (Δ):

Roots:

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About Quadratic Equations

A quadratic equation is a second-degree polynomial equation commonly used in physics, engineering, finance, and mathematics to model real-world problems.

How This Solver Works

The calculator applies the quadratic formula: x = (−b ± √Δ) / 2a, where Δ = b² − 4ac. Based on the value of the discriminant, the tool determines whether the roots are real, repeated, or complex.

Interpretation

Δ > 0 → Two distinct real roots
Δ = 0 → One repeated real root
Δ < 0 → Two complex conjugate roots

FAQs

What if a = 0? The equation becomes linear, not quadratic.
Are complex roots useful? Yes, especially in engineering and signal analysis.
Is this exact? Results are mathematically accurate, rounded for readability.