-12n-4=6n^2

Solution for -12n-4=6n^2 equation:

-12n-4=6n^2

We move all terms to the left:

-12n-4-(6n^2)=0

determiningTheFunctionDomain
-6n^2-12n-4=0

a = -6; b = -12; c = -4;
Δ = b2-4ac
Δ = -122-4·(-6)·(-4)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{3}}{2*-6}=\frac{12-4\sqrt{3}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{3}}{2*-6}=\frac{12+4\sqrt{3}}{-12}
$