Quadratic Equation Solver

What is the Quadratic Equation Solver?

A quadratic equation is any equation in the form ax² + bx + c = 0, where x is the unknown. You run into these constantly in math class, physics, and engineering — anywhere a parabola shows up. CalciHub's solver takes your three coefficients, applies the quadratic formula, and gives you the roots instantly. It also tells you whether the roots are real or complex, which saves you a few steps when the discriminant goes negative.

How Does It Work?

The quadratic formula works by plugging your a, b, and c values into an expression that produces two possible answers. The part under the square root — called the discriminant — tells you a lot before you even finish the calculation. Positive discriminant means two real roots. Zero means one repeated root. Negative means you're in complex number territory.

x = (-b ± √(b² - 4ac)) / 2a

• a = coefficient of x²

• b = coefficient of x

• c = constant term

• ± = the formula gives two answers, one with + and one with −

• √(b² - 4ac) = discriminant under the root

How to Use CalciHub's Quadratic Equation Solver

1. Enter the value of a (the x² coefficient) in the first field.

2. Enter b (the x coefficient) in the second field.

3. Enter c (the constant) in the third field.

4. Hit Calculate — the solver returns both roots and shows the discriminant.

5. If the roots are complex, they appear in a + bi form.

Tip: If you're working backwards from a graph, you can read the roots off the x-axis and reverse-engineer the coefficients.

A Quick Example

Say you need to solve x² − 5x + 6 = 0. You enter a = 1, b = −5, c = 6. The discriminant is (−5)² − 4(1)(6) = 25 − 24 = 1. Since the discriminant is positive, there are two real roots. The formula gives x = (5 ± 1) / 2, so x = 3 and x = 2. You can verify these by factoring: (x − 2)(x − 3) = 0. The solver produces the same result in under a second.

When the discriminant is a perfect square, the roots are whole numbers — and factoring would have worked just as well.

Frequently Asked Questions