Overview
Quadratic equations have the form ax² + bx + c = 0. The quadratic formula always works when a ≠ 0 and tells you how many real solutions exist via the discriminant.
Identify a, b, and c
Write the equation as ax² + bx + c = 0 before substituting into the formula.
Read the discriminant
Δ > 0 two real roots; Δ = 0 one; Δ < 0 none in the reals.
Check by substitution
Plug each root back into ax² + bx + c to confirm you get approximately zero.
Try the calculator
Use the free Quadratic Formula Calculator for live numbers, then come back to this guide anytime you need a quick refresher.