2n^2=64-8n

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

2n^2=64-8n

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

2n^2+8n-64=0

a = 2; b = 8; c = -64;
Δ = b2-4ac
Δ = 82-4·2·(-64)
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{-(8)-24}{2*2}=\frac{-32}{4}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+24}{2*2}=\frac{16}{4}
=4
$