33W=12w^2-135

Solution for 33W=12w^2-135 equation:

33=12W^2-135

We move all terms to the left:

33-(12W^2-135)=0

We get rid of parentheses

-12W^2+135+33=0

We add all the numbers together, and all the variables

-12W^2+168=0

a = -12; b = 0; c = +168;
Δ = b2-4ac
Δ = 02-4·(-12)·168
Δ = 8064
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:

$\sqrt{\Delta}=\sqrt{8064}=\sqrt{576*14}=\sqrt{576}*\sqrt{14}=24\sqrt{14}$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{14}}{2*-12}=\frac{0-24\sqrt{14}}{-24}
=-\frac{24\sqrt{14}}{-24}
=-\frac{\sqrt{14}}{-1}
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{14}}{2*-12}=\frac{0+24\sqrt{14}}{-24}
=\frac{24\sqrt{14}}{-24}
=\frac{\sqrt{14}}{-1}
$