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.

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