6n2-12n-96=-6

Solution for 6n2-12n-96=-6 equation:

6n^2-12n-96=-6

We move all terms to the left:

6n^2-12n-96-(-6)=0

We add all the numbers together, and all the variables

6n^2-12n-90=0

a = 6; b = -12; c = -90;
Δ = b2-4ac
Δ = -122-4·6·(-90)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-48}{2*6}=\frac{-36}{12}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+48}{2*6}=\frac{60}{12}
=5
$