What is the discriminant?

The discriminant is b² - 4ac. If > 0: two distinct real roots. If = 0: one repeated real root. If < 0: no real roots (two complex roots).

If a = 0, the equation is not quadratic — it becomes linear (bx + c = 0) with solution x = -c/b.

How do I find the second root?

x₂ = (-b - √(b² - 4ac)) / (2a). Both roots always add up to -b/a and multiply to c/a (Vieta's formulas).

Quadratic Formula Calculator

The Quadratic Formula Calculator solves any quadratic equation of the form ax² + bx + c = 0. Enter the coefficients a, b, and c and get the two roots (solutions) instantly. The calculator returns the larger of the two roots — use the discriminant (b² - 4ac) to determine whether the roots are real and distinct, equal, or complex.

Coefficient a (x²)

Coefficient b (x)

Coefficient c (constant)

How to Use This Calculator

1
Enter coefficient a (the number in front of x²).
2
Enter coefficient b (the number in front of x).
3
Enter coefficient c (the constant term).
4
Click Calculate to see the larger root (x₁). The smaller root x₂ = (-b - √discriminant) / 2a.

Frequently Asked Questions

x = (-b ± √(b² - 4ac)) / (2a). This gives two solutions (roots) for any quadratic equation ax² + bx + c = 0.

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