-6-12n^2=-396

Solution for -6-12n^2=-396 equation:

-6-12n^2=-396

We move all terms to the left:

-6-12n^2-(-396)=0

We add all the numbers together, and all the variables

-12n^2+390=0

a = -12; b = 0; c = +390;
Δ = b2-4ac
Δ = 02-4·(-12)·390
Δ = 18720
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:

$\sqrt{\Delta}=\sqrt{18720}=\sqrt{144*130}=\sqrt{144}*\sqrt{130}=12\sqrt{130}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{130}}{2*-12}=\frac{0-12\sqrt{130}}{-24}
=-\frac{12\sqrt{130}}{-24}
=-\frac{\sqrt{130}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{130}}{2*-12}=\frac{0+12\sqrt{130}}{-24}
=\frac{12\sqrt{130}}{-24}
=\frac{\sqrt{130}}{-2}
$