144x^2-120x=150

Solution for 144x^2-120x=150 equation:

144x^2-120x=150

We move all terms to the left:

144x^2-120x-(150)=0

a = 144; b = -120; c = -150;
Δ = b2-4ac
Δ = -1202-4·144·(-150)
Δ = 100800
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:

$\sqrt{\Delta}=\sqrt{100800}=\sqrt{14400*7}=\sqrt{14400}*\sqrt{7}=120\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120\sqrt{7}}{2*144}=\frac{120-120\sqrt{7}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120\sqrt{7}}{2*144}=\frac{120+120\sqrt{7}}{288}
$