x^2-x-14=0 — step-by-step solution

Let's solve in

ℝ

x^{2} - x - 14 = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-1)}^{2} - 4 \cdot 1 \cdot (-14)

Δ = 1 - 4 \cdot (-14)

Δ = 1 + 56

Δ = 57

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

For the second solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

Solution found:

x = \frac{1 - \sqrt{57}}{2}

Solution obtained:

x = \frac{\sqrt{57} + 1}{2}

▶Solution:

x = {\frac{1 - \sqrt{57}}{2}, \frac{\sqrt{57} + 1}{2}}

The numeric value of:

x = {\frac{1 - \sqrt{57}}{2}, \frac{\sqrt{57} + 1}{2}}

equals:

x = {\frac{1 + \approx -7.5498}{2}, \frac{\approx 7.5498 + 1}{2}}

x = {- \frac{\approx 6.5498}{2}, \frac{\approx 8.5498}{2}}

▷

x = {\approx -3.2749, \approx 4.2749}