2n^2=2n+60

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

2n^2=2n+60

We move all terms to the left:

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

We get rid of parentheses

2n^2-2n-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:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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