w(w+8)=256

Solution for w(w+8)=256 equation:

w(w+8)=256

We move all terms to the left:

w(w+8)-(256)=0

We multiply parentheses

w^2+8w-256=0

a = 1; b = 8; c = -256;
Δ = b2-4ac
Δ = 82-4·1·(-256)
Δ = 1088
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{17}}{2*1}=\frac{-8-8\sqrt{17}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{17}}{2*1}=\frac{-8+8\sqrt{17}}{2}
$