(x+8)(x)-8=0

Solution for (x+8)(x)-8=0 equation:

(x+8)(x)-8=0

We multiply parentheses

x^2+8x-8=0

a = 1; b = 8; c = -8;
Δ = b2-4ac
Δ = 82-4·1·(-8)
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*1}=\frac{-8-4\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*1}=\frac{-8+4\sqrt{6}}{2}
$