Math solver
Standalone tool pageQuadratic Equation Solver
Solve any quadratic equation instantly. Get step-by-step discriminant and root analysis.
Output
Equation results
Delta (Δ)
Root x₁
Root x₂
Enter coefficients and solve to see results.
How It Works
Enter the coefficients a, b, and c into the corresponding fields. The tool will calculate the discriminant (Δ) and then find the roots (x₁ and x₂) using the quadratic formula. It automatically detects if the roots are real, repeated, or complex.
Example
For the equation x² - 5x + 6 = 0: a=1, b=-5, c=6. The discriminant is (-5)² - 4(1)(6) = 25 - 24 = 1. The roots are x₁ = (5+1)/2 = 3 and x₂ = (5-1)/2 = 2.
Frequently Asked Questions
What is a quadratic equation?
A quadratic equation is a second-degree polynomial equation in a single variable x, with a non-zero coefficient for x². The general form is ax² + bx + c = 0.
How do you solve a quadratic equation?
You can solve it using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The term b² - 4ac is called the discriminant (Δ).
What does the discriminant (Δ) tell us?
If Δ > 0, there are two distinct real roots. If Δ = 0, there is exactly one real root (repeated). If Δ < 0, there are no real roots, only complex ones.
Can this solver handle complex roots?
Yes, if the discriminant is negative, the solver will provide the roots in the form of a + bi and a - bi.
What happens if 'a' is zero?
If a = 0, the equation is no longer quadratic; it becomes a linear equation (bx + c = 0). This solver requires 'a' to be non-zero to apply quadratic logic.