Math

Quadratic Equation Solver

Solve ax² + bx + c = 0.

Input Values

Adjust parameters below

RESULT
Root x₁
2
NUMBER
Root x₂
1
Discriminant (Δ)
1
💡

Step-by-Step Solution

How this result was calculated

1

Identify coefficients: a=1, b=-3, c=2

2

Calculate Discriminant (Δ) = b² - 4ac

3

Δ = (-3)² - 4(1)(2) = 1

4

Apply Quadratic Formula: x = (-b ± √Δ) / 2a

5

x = (3 ± √1) / 2

6

x₁ = (3 + 1.0000) / 2 = 2.0000

7

x₂ = (3 - 1.0000) / 2 = 1.0000

How It Works

Guide and Formula

Quadratic Formula Solver

This calculator solves equations of the form ax² + bx + c = 0.

The Quadratic Formula:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Understanding the Discriminant (Δ = b² - 4ac)

Δ > 0: Two distinct real roots
Δ = 0: One real root (repeated)
Δ < 0: Complex roots (no real solutions)

How it Works

1. Identify coefficients: Extract a, b, and c from your equation

2. Calculate discriminant: Compute Δ = b² - 4ac

3. Apply formula: Use the quadratic formula to find x values

4. Interpret results: Based on the discriminant value

?FAQs

What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation in the form ax² + bx + c = 0, where a ≠ 0.

What happens if the discriminant is negative?

If the discriminant is negative, the equation has no real solutions—only complex roots involving imaginary numbers.

Can the coefficient 'a' be zero?

No, if 'a' is zero, it's not a quadratic equation—it becomes a linear equation (bx + c = 0).

What is the sum and product of roots?

For roots x₁ and x₂: Sum = -b/a and Product = c/a.

Quadratic Equation Solver - EasyCalcHub