3n^2=13n+30

Solution for 3n^2=13n+30 equation:

3n^2=13n+30

We move all terms to the left:

3n^2-(13n+30)=0

We get rid of parentheses

3n^2-13n-30=0

a = 3; b = -13; c = -30;
Δ = b2-4ac
Δ = -132-4·3·(-30)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-23}{2*3}=\frac{-10}{6}
=-1+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+23}{2*3}=\frac{36}{6}
=6
$