Standard Quadratic Suite
Quadratic Formula Solver
Find the roots of any quadratic equation instantly. Our solver calculates the discriminant and provides both real roots.
Quadratic Solver
Input Coefficients: ax² + bx + c = 0
FORMULA: x = (-b ± √D) / 2a
Discriminant (D)1(Two Real Roots)
Roots (x)
x₁: 3|x₂: 2
If D > 0, there are two distinct real roots. If D = 0, there is exactly one real root. If D < 0, there are two complex roots.
What is the Formula?
The quadratic formula is used to find the solutions (roots) of a quadratic equation. It is derived from completing the square of the standard form equation.
x = -b ± √(b² - 4ac) / 2a
The Quadratic Formula
Discriminant (D)
D > 0
Two distinct real roots (The parabola crosses the x-axis twice).
D = 0
One real root (The parabola's vertex touches the x-axis).
D < 0
Two complex roots (The parabola never touches the x-axis).