132x=180+24x^2

Solution for 132x=180+24x^2 equation:

132x=180+24x^2

We move all terms to the left:

132x-(180+24x^2)=0

We get rid of parentheses

-24x^2+132x-180=0

a = -24; b = 132; c = -180;
Δ = b2-4ac
Δ = 1322-4·(-24)·(-180)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-12}{2*-24}=\frac{-144}{-48}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+12}{2*-24}=\frac{-120}{-48}
=2+1/2
$