2x^2=2x+60

Solution for 2x^2=2x+60 equation:

2x^2=2x+60

We move all terms to the left:

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

We get rid of parentheses

2x^2-2x-60=0

a = 2; b = -2; c = -60;
Δ = b2-4ac
Δ = -22-4·2·(-60)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*2}=\frac{24}{4}
=6
$