solve x^2-5x+6=0 — step-by-step solution

Let's solve in

ℝ

x^{2} - 5 x + 6 = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-5)}^{2} - 4 \cdot 1 \cdot 6

Δ = 25 - 4 \cdot 6

Δ = 25 - 24

Δ = 1

Since

Δ > 0

, the equation has two solutions:

Solution first:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{5 - 1}{2}

x1 = \frac{4}{2}

x1 = 2

For the 2nd solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{5 + 1}{2}

x2 = \frac{6}{2}

x2 = 3

Solution found:

x = 2

Solution obtained:

x = 3

▷Answer: $x = {2, 3}$