0=60-64x+12x^2

Solution for 0=60-64x+12x^2 equation:

0=60-64x+12x^2

We move all terms to the left:

0-(60-64x+12x^2)=0

We add all the numbers together, and all the variables

-(60-64x+12x^2)=0

We get rid of parentheses

-12x^2+64x-60=0

a = -12; b = 64; c = -60;
Δ = b2-4ac
Δ = 642-4·(-12)·(-60)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{19}}{2*-12}=\frac{-64-8\sqrt{19}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{19}}{2*-12}=\frac{-64+8\sqrt{19}}{-24}
$