(12n+12)12n=36

Solution for (12n+12)12n=36 equation:

(12n+12)12n=36

We move all terms to the left:

(12n+12)12n-(36)=0

We multiply parentheses

144n^2+144n-36=0

a = 144; b = 144; c = -36;
Δ = b2-4ac
Δ = 1442-4·144·(-36)
Δ = 41472
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:

$\sqrt{\Delta}=\sqrt{41472}=\sqrt{20736*2}=\sqrt{20736}*\sqrt{2}=144\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144\sqrt{2}}{2*144}=\frac{-144-144\sqrt{2}}{288}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144\sqrt{2}}{2*144}=\frac{-144+144\sqrt{2}}{288}
$