3n^2-60=8n

Solution for 3n^2-60=8n equation:

3n^2-60=8n

We move all terms to the left:

3n^2-60-(8n)=0

a = 3; b = -8; c = -60;
Δ = b2-4ac
Δ = -82-4·3·(-60)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28}{2*3}=\frac{-20}{6}
=-3+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28}{2*3}=\frac{36}{6}
=6
$