15x^2-5x=60

Solution for 15x^2-5x=60 equation:

15x^2-5x=60

We move all terms to the left:

15x^2-5x-(60)=0

a = 15; b = -5; c = -60;
Δ = b2-4ac
Δ = -52-4·15·(-60)
Δ = 3625
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:

$\sqrt{\Delta}=\sqrt{3625}=\sqrt{25*145}=\sqrt{25}*\sqrt{145}=5\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{145}}{2*15}=\frac{5-5\sqrt{145}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{145}}{2*15}=\frac{5+5\sqrt{145}}{30}
$