X^2+8x+16=128

Solution for X^2+8x+16=128 equation:

X^2+8X+16=128

We move all terms to the left:

X^2+8X+16-(128)=0

We add all the numbers together, and all the variables

X^2+8X-112=0

a = 1; b = 8; c = -112;
Δ = b2-4ac
Δ = 82-4·1·(-112)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{2}}{2*1}=\frac{-8-16\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{2}}{2*1}=\frac{-8+16\sqrt{2}}{2}
$