15x^2-5x=120

Solution for 15x^2-5x=120 equation:

15x^2-5x=120

We move all terms to the left:

15x^2-5x-(120)=0

a = 15; b = -5; c = -120;
Δ = b2-4ac
Δ = -52-4·15·(-120)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-85}{2*15}=\frac{-80}{30}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+85}{2*15}=\frac{90}{30}
=3
$