15x=12x^2-180

Solution for 15x=12x^2-180 equation:

15x=12x^2-180

We move all terms to the left:

15x-(12x^2-180)=0

We get rid of parentheses

-12x^2+15x+180=0

a = -12; b = 15; c = +180;
Δ = b2-4ac
Δ = 152-4·(-12)·180
Δ = 8865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8865}=\sqrt{9*985}=\sqrt{9}*\sqrt{985}=3\sqrt{985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{985}}{2*-12}=\frac{-15-3\sqrt{985}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{985}}{2*-12}=\frac{-15+3\sqrt{985}}{-24}
$