-12n-12=n^2

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

-12n-12=n^2

We move all terms to the left:

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

determiningTheFunctionDomain
-n^2-12n-12=0

We add all the numbers together, and all the variables

-1n^2-12n-12=0

a = -1; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·(-1)·(-12)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{6}}{2*-1}=\frac{12-4\sqrt{6}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{6}}{2*-1}=\frac{12+4\sqrt{6}}{-2}
$