3n^2-12n-32=-8

Solution for 3n^2-12n-32=-8 equation:

3n^2-12n-32=-8

We move all terms to the left:

3n^2-12n-32-(-8)=0

We add all the numbers together, and all the variables

3n^2-12n-24=0

a = 3; b = -12; c = -24;
Δ = b2-4ac
Δ = -122-4·3·(-24)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{3}}{2*3}=\frac{12-12\sqrt{3}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{3}}{2*3}=\frac{12+12\sqrt{3}}{6}
$