2w^2-2w=32

Solution for 2w^2-2w=32 equation:

2w^2-2w=32

We move all terms to the left:

2w^2-2w-(32)=0

a = 2; b = -2; c = -32;
Δ = b2-4ac
Δ = -22-4·2·(-32)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{65}}{2*2}=\frac{2-2\sqrt{65}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{65}}{2*2}=\frac{2+2\sqrt{65}}{4}
$