512=2w^2

Solution for 512=2w^2 equation:

512=2w^2

We move all terms to the left:

512-(2w^2)=0

a = -2; b = 0; c = +512;
Δ = b2-4ac
Δ = 02-4·(-2)·512
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64}{2*-2}=\frac{-64}{-4}
=+16
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64}{2*-2}=\frac{64}{-4}
=-16
$