3n^2=12n+36

Solution for 3n^2=12n+36 equation:

3n^2=12n+36

We move all terms to the left:

3n^2-(12n+36)=0

We get rid of parentheses

3n^2-12n-36=0

a = 3; b = -12; c = -36;
Δ = b2-4ac
Δ = -122-4·3·(-36)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*3}=\frac{-12}{6}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*3}=\frac{36}{6}
=6
$