Quadratic Formula Calculator

All math tools

Step-by-step application of the quadratic formula to solve equations.

Input Parameters

Coefficient a

Coefficient b

Constant c

Step-by-Step Solution

Quadratic Formula:

x = −b ± √b² − 4ac
2a

Substituting values:

x = [-(-5) ± √(-5² - 4(1)(6))] / 2(1)

Calculate Discriminant (b² - 4ac):

25 - 24 = 1

Simplify:

x = [5 ± 1.0000] / 2

Final Solutions:

x13.0000

x22.0000

About this calculator

The Quadratic Formula

The quadratic formula is a universal way to solve any quadratic equation. It is derived by 'completing the square' on the general quadratic equation ax² + bx + c = 0. It always works, even when factoring is impossible or the roots are irrational or complex.

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Pro Tips

Order: Always ensure your equation is in standard form (ax² + bx + c = 0) before identifying a, b, and c.
Signs: Be extremely careful with negative signs, especially in the 4ac term.
Simplification: If the number inside the square root is a perfect square, your solutions will be rational.

Fun Facts

"Al-Khwarizmi, often called the 'father of algebra', developed the earliest geometric methods for solving these equations in the 9th century."
"You can sing the quadratic formula to the tune of 'Pop Goes the Weasel' to help memorize it."

Formula: x = [-b ± √(b² - 4ac)] / 2a