0=8+8x+x^2

Solution for 0=8+8x+x^2 equation:

0=8+8x+x^2

We move all terms to the left:

0-(8+8x+x^2)=0

We add all the numbers together, and all the variables

-(8+8x+x^2)=0

We get rid of parentheses

-x^2-8x-8=0

We add all the numbers together, and all the variables

-1x^2-8x-8=0

a = -1; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·(-1)·(-8)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{2}}{2*-1}=\frac{8-4\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{2}}{2*-1}=\frac{8+4\sqrt{2}}{-2}
$