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

Let's solve in

ℝ

x^{2} + x - 6 = 0

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = 1 - 4 \cdot 1 \cdot -6

Δ = 1 - 4 \cdot -6

Δ = 1 + 24

Δ = 25

Δ > 0

, the equation has two solutions:

Solution first:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{- 1 - \sqrt{25}}{2}

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

x1 = - \frac{6}{2}

x1 = -3

For the 2nd solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{- 1 + \sqrt{25}}{2}

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

x2 = \frac{4}{2}

x2 = 2

Solution obtained:

x = -3

Solution obtained:

x = 2

▷Result: $x = {-3, 2}$