2w(2w+16)=256

Solution for 2w(2w+16)=256 equation:

2w(2w+16)=256

We move all terms to the left:

2w(2w+16)-(256)=0

We multiply parentheses

4w^2+32w-256=0

a = 4; b = 32; c = -256;
Δ = b2-4ac
Δ = 322-4·4·(-256)
Δ = 5120
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:

$\sqrt{\Delta}=\sqrt{5120}=\sqrt{1024*5}=\sqrt{1024}*\sqrt{5}=32\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32\sqrt{5}}{2*4}=\frac{-32-32\sqrt{5}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32\sqrt{5}}{2*4}=\frac{-32+32\sqrt{5}}{8}
$