3(n+12)n=3

Solution for 3(n+12)n=3 equation:

3(n+12)n=3

We move all terms to the left:

3(n+12)n-(3)=0

We multiply parentheses

3n^2+36n-3=0

a = 3; b = 36; c = -3;
Δ = b2-4ac
Δ = 362-4·3·(-3)
Δ = 1332
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{37}}{2*3}=\frac{-36-6\sqrt{37}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{37}}{2*3}=\frac{-36+6\sqrt{37}}{6}
$