2w+2w(w+8)=256

Solution for 2w+2w(w+8)=256 equation:

2w+2w(w+8)=256

We move all terms to the left:

2w+2w(w+8)-(256)=0

We multiply parentheses

2w^2+2w+16w-256=0

We add all the numbers together, and all the variables

2w^2+18w-256=0

a = 2; b = 18; c = -256;
Δ = b2-4ac
Δ = 182-4·2·(-256)
Δ = 2372
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:

$\sqrt{\Delta}=\sqrt{2372}=\sqrt{4*593}=\sqrt{4}*\sqrt{593}=2\sqrt{593}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{593}}{2*2}=\frac{-18-2\sqrt{593}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{593}}{2*2}=\frac{-18+2\sqrt{593}}{4}
$