W^3-4w^2=32w

Solution for W^3-4w^2=32w equation:

^3-4W^2=32W

We move all terms to the left:

^3-4W^2-(32W)=0

We add all the numbers together, and all the variables

-4W^2-32W=0

a = -4; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-4)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-4}=\frac{0}{-8}
=0
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-4}=\frac{64}{-8}
=-8
$