Quadratic Equation Solver

Solve ax² + bx + c = 0 with step-by-step solution

Formula

x = (-b ± √(b² - 4ac)) / 2a

The quadratic formula gives roots of any quadratic equation. Discriminant (Δ = b² - 4ac) determines root type: Δ > 0 (two real), Δ = 0 (one real), Δ < 0 (complex).

How to Calculate Manually

1
Identify coefficients a, b, c from ax² + bx + c = 0
2
Calculate discriminant: Δ = b² - 4ac
3
If Δ > 0: two real roots using ±√Δ
4
If Δ = 0: one real root (repeated)
5
If Δ < 0: two complex roots with ±i√|Δ|
6
If a = 0: solve linear equation bx + c = 0

Reference Table

Equation	a	b	c	Discriminant	Roots
x² - 5x + 6 = 0	1	-5	6	1	2, 3
x² - 4x + 4 = 0	1	-4	4	0	2 (repeated)
x² + x + 1 = 0	1	1	1	-3	-0.5 ± 0.866i
2x² - 8x + 6 = 0	2	-8	6	16	1, 3

Quadratic Equation Solver: Complete Guide to the Quadratic Formula

The quadratic formula is one of the most important tools in algebra. It provides a universal method for solving any quadratic equation of the form ax² + bx + c = 0. Understanding how to use it and interpret the discriminant...

Frequently Asked Questions

What is the quadratic formula? x = (-b ± √(b² - 4ac)) / 2a. The discriminant (b² - 4ac) determines the nature of roots.: x = (-b ± √(b² - 4ac)) / 2a. The discriminant (b² - 4ac) determines the nature of roots.
What does the discriminant tell you? Discriminant > 0: two real roots. Discriminant = 0: one real root (repeated). Discriminant < 0: two complex conjugate roots.: Discriminant > 0: two real roots. Discriminant = 0: one real root (repeated). Discriminant < 0: two complex conjugate roots.
What if a = 0? If a = 0, it's a linear equation (bx + c = 0), not quadratic. This calculator handles that case and solves for x = -c/b.: If a = 0, it's a linear equation (bx + c = 0), not quadratic. This calculator handles that case and solves for x = -c/b.

Calculator

Formula

Formula

How to Calculate Manually

Reference Table

Quadratic Equation Solver: Complete Guide to the Quadratic Formula

Frequently Asked Questions

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