n^2-8=-8n

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

n^2-8=-8n

We move all terms to the left:

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

We get rid of parentheses

n^2+8n-8=0

a = 1; b = 8; c = -8;
Δ = b2-4ac
Δ = 82-4·1·(-8)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*1}=\frac{-8-4\sqrt{6}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*1}=\frac{-8+4\sqrt{6}}{2}
$