-2=n(n-8)

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



-2=n(n-8)
We move all terms to the left:
-2-(n(n-8))=0
We calculate terms in parentheses: -(n(n-8)), so:
n(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} $

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