3n^2-135=12n

Solution for 3n^2-135=12n equation:

3n^2-135=12n

We move all terms to the left:

3n^2-135-(12n)=0

a = 3; b = -12; c = -135;
Δ = b2-4ac
Δ = -122-4·3·(-135)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-42}{2*3}=\frac{-30}{6}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+42}{2*3}=\frac{54}{6}
=9
$