-2=-1n(n-8)

Solution for -2=-1n(n-8) equation:

-2=-1n(n-8)

We move all terms to the left:

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


We calculate terms in parentheses: -(-1n(n-8)), so:

-1n(n-8)

We multiply parentheses

-n^2+8n

We add all the numbers together, and all the variables

-1n^2+8n

Back to the equation:

-(-1n^2+8n)


We get rid of parentheses

1n^2-8n-2=0

We add all the numbers together, and all the variables

n^2-8n-2=0

a = 1; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·1·(-2)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{2}}{2*1}=\frac{8-6\sqrt{2}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{2}}{2*1}=\frac{8+6\sqrt{2}}{2}
$