How to Solve Quadratic Equations Step by Step
A quadratic equation looks like ax² + bx + c = 0. Our solver handles them instantly, but here's the method it follows — worth learning for exams.
Step 1: Write in standard form
Move everything to one side so the equation reads ax² + bx + c = 0. For example, x² − 5x + 6 = 0 is already in standard form.
Step 2: Identify a, b and c
Read off the coefficients: in x² − 5x + 6 = 0, a = 1, b = −5, c = 6.
Step 3: Compute the discriminant
Δ = b² − 4ac. Here Δ = 25 − 24 = 1. If Δ > 0 there are two real roots; if Δ = 0 one repeated root; if Δ < 0 the roots are complex.
Step 4: Apply the quadratic formula
x = (−b ± √Δ) / 2a = (5 ± 1) / 2, giving x = 3 or x = 2.
Try it yourself
Type any quadratic into the solver below and compare its steps with yours.