64=2n^2-8

Solution for 64=2n^2-8 equation:

64=2n^2-8

We move all terms to the left:

64-(2n^2-8)=0

We get rid of parentheses

-2n^2+8+64=0

We add all the numbers together, and all the variables

-2n^2+72=0

a = -2; b = 0; c = +72;
Δ = b2-4ac
Δ = 02-4·(-2)·72
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*-2}=\frac{-24}{-4}
=+6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*-2}=\frac{24}{-4}
=-6
$