0=12x^2-8x-60

Solution for 0=12x^2-8x-60 equation:

0=12x^2-8x-60

We move all terms to the left:

0-(12x^2-8x-60)=0

We add all the numbers together, and all the variables

-(12x^2-8x-60)=0

We get rid of parentheses

-12x^2+8x+60=0

a = -12; b = 8; c = +60;
Δ = b2-4ac
Δ = 82-4·(-12)·60
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{46}}{2*-12}=\frac{-8-8\sqrt{46}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{46}}{2*-12}=\frac{-8+8\sqrt{46}}{-24}
$