120=2n^2-8

Solution for 120=2n^2-8 equation:

120=2n^2-8

We move all terms to the left:

120-(2n^2-8)=0

We get rid of parentheses

-2n^2+8+120=0

We add all the numbers together, and all the variables

-2n^2+128=0

a = -2; b = 0; c = +128;
Δ = b2-4ac
Δ = 02-4·(-2)·128
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*-2}=\frac{-32}{-4}
=+8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*-2}=\frac{32}{-4}
=-8
$