30n^2=48+36n

Solution for 30n^2=48+36n equation:

30n^2=48+36n

We move all terms to the left:

30n^2-(48+36n)=0

We add all the numbers together, and all the variables

30n^2-(36n+48)=0

We get rid of parentheses

30n^2-36n-48=0

a = 30; b = -36; c = -48;
Δ = b2-4ac
Δ = -362-4·30·(-48)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-84}{2*30}=\frac{-48}{60}
=-4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+84}{2*30}=\frac{120}{60}
=2
$