w2=512

Solution for w2=512 equation:

w2=512

We move all terms to the left:

w2-(512)=0

We add all the numbers together, and all the variables

w^2-512=0

a = 1; b = 0; c = -512;
Δ = b2-4ac
Δ = 02-4·1·(-512)
Δ = 2048
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:

$\sqrt{\Delta}=\sqrt{2048}=\sqrt{1024*2}=\sqrt{1024}*\sqrt{2}=32\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{2}}{2*1}=\frac{0-32\sqrt{2}}{2}
=-\frac{32\sqrt{2}}{2}
=-16\sqrt{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{2}}{2*1}=\frac{0+32\sqrt{2}}{2}
=\frac{32\sqrt{2}}{2}
=16\sqrt{2}
$