The Quadratic Formula Explained

The quadratic formula solves any quadratic equation, even when factoring is hard or impossible with whole numbers.

Quick idea

For ax squared plus bx plus c equals zero, identify a, b, and c, then substitute them carefully into the formula.

Steps

1. Write the equation in standard form equal to zero.
2. Identify a, b, and c.
3. Substitute into the quadratic formula.
4. Simplify the discriminant, square root, numerator, and denominator.

Worked example

Solve x squared minus 5x plus 6 equals zero.

Full solution

Step-by-step walkthrough

Step 1

Here a equals 1, b equals -5, and c equals 6.

Step 2

Substituting gives x equals 2 or x equals 3.

Step 3

Those are the same answers you would get by factoring.

Common mistake

Be careful when b is negative. The formula starts with negative b, so a negative b becomes positive.

Practice problems

1. Solve x^2 - 4x + 3 = 0.
2. Solve x^2 + 2x - 8 = 0.
3. Solve 2x^2 - 8x + 6 = 0.

Answers

1. x = 1 or 3
2. x = 2 or -4
3. x = 1 or 3

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Factor Quadratics
• How to Simplify Exponents
• How to Find Missing Angles