6n^2=30+24n

Solution for 6n^2=30+24n equation:

6n^2=30+24n

We move all terms to the left:

6n^2-(30+24n)=0

We add all the numbers together, and all the variables

6n^2-(24n+30)=0

We get rid of parentheses

6n^2-24n-30=0

a = 6; b = -24; c = -30;
Δ = b2-4ac
Δ = -242-4·6·(-30)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-36}{2*6}=\frac{-12}{12}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+36}{2*6}=\frac{60}{12}
=5
$