(12n+2)12n=36

Solution for (12n+2)12n=36 equation:

(12n+2)12n=36

We move all terms to the left:

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

We multiply parentheses

144n^2+24n-36=0

a = 144; b = 24; c = -36;
Δ = b2-4ac
Δ = 242-4·144·(-36)
Δ = 21312
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:

$\sqrt{\Delta}=\sqrt{21312}=\sqrt{576*37}=\sqrt{576}*\sqrt{37}=24\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{37}}{2*144}=\frac{-24-24\sqrt{37}}{288}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{37}}{2*144}=\frac{-24+24\sqrt{37}}{288}
$