15x^2-120x=180

Solution for 15x^2-120x=180 equation:

15x^2-120x=180

We move all terms to the left:

15x^2-120x-(180)=0

a = 15; b = -120; c = -180;
Δ = b2-4ac
Δ = -1202-4·15·(-180)
Δ = 25200
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:

$\sqrt{\Delta}=\sqrt{25200}=\sqrt{3600*7}=\sqrt{3600}*\sqrt{7}=60\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-60\sqrt{7}}{2*15}=\frac{120-60\sqrt{7}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+60\sqrt{7}}{2*15}=\frac{120+60\sqrt{7}}{30}
$