-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 add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1n^2-(-8n-8)=0

We get rid of parentheses

-1n^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}
$