60=24x^2-2x

Solution for 60=24x^2-2x equation:

60=24x^2-2x

We move all terms to the left:

60-(24x^2-2x)=0

We get rid of parentheses

-24x^2+2x+60=0

a = -24; b = 2; c = +60;
Δ = b2-4ac
Δ = 22-4·(-24)·60
Δ = 5764
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:

$\sqrt{\Delta}=\sqrt{5764}=\sqrt{4*1441}=\sqrt{4}*\sqrt{1441}=2\sqrt{1441}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1441}}{2*-24}=\frac{-2-2\sqrt{1441}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1441}}{2*-24}=\frac{-2+2\sqrt{1441}}{-48}
$