# Question #ae517

Oct 24, 2016

$x = \pm 2 \sqrt{7}$

#### Explanation:

$f \left(x\right) = g \left(x\right)$

$\implies x + 5 = \frac{3}{x - 5}$

$\implies \left(x + 5\right) \left(x - 5\right) = 3$

$\implies {x}^{2} - 25 = 3$

At this point it would be simplest to just add $25$ to both sides and take a square root, but as the question refers to the quadratic formula, we will instead put it in standard form and proceed in that manner.

$\implies {x}^{2} - 28 = 0$

$\implies 1 {x}^{2} + 0 x - 28 = 0$

$\implies x = \frac{- 0 \pm \sqrt{{0}^{2} - 4 \left(1\right) \left(- 28\right)}}{2 \left(1\right)}$

$= \frac{\pm 4 \sqrt{7}}{2}$

$= \pm 2 \sqrt{7}$