-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

Back to the equation:

-(n^2-8n)


We get rid of parentheses

-n^2+8n-2=0

We add all the numbers together, and all the variables

-1n^2+8n-2=0

a = -1; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·(-1)·(-2)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{14}}{2*-1}=\frac{-8-2\sqrt{14}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{14}}{2*-1}=\frac{-8+2\sqrt{14}}{-2}
$