2w^2=165-32

Solution for 2w^2=165-32 equation:

2w^2=165-32

We move all terms to the left:

2w^2-(165-32)=0

We add all the numbers together, and all the variables

2w^2-133=0

a = 2; b = 0; c = -133;
Δ = b2-4ac
Δ = 02-4·2·(-133)
Δ = 1064
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:

$\sqrt{\Delta}=\sqrt{1064}=\sqrt{4*266}=\sqrt{4}*\sqrt{266}=2\sqrt{266}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{266}}{2*2}=\frac{0-2\sqrt{266}}{4}
=-\frac{2\sqrt{266}}{4}
=-\frac{\sqrt{266}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{266}}{2*2}=\frac{0+2\sqrt{266}}{4}
=\frac{2\sqrt{266}}{4}
=\frac{\sqrt{266}}{2}
$