-(n-7)-n=-8(6+n)6n

Solution for -(n-7)-n=-8(6+n)6n equation:

-(n-7)-n=-8(6+n)6n

We move all terms to the left:

-(n-7)-n-(-8(6+n)6n)=0

We add all the numbers together, and all the variables

-(n-7)-n-(-8(n+6)6n)=0

We add all the numbers together, and all the variables

-1n-(n-7)-(-8(n+6)6n)=0

We get rid of parentheses

-1n-n-(-8(n+6)6n)+7=0


We calculate terms in parentheses: -(-8(n+6)6n), so:

-8(n+6)6n

We multiply parentheses

-48n^2-288n

Back to the equation:

-(-48n^2-288n)


We add all the numbers together, and all the variables

-(-48n^2-288n)-2n+7=0

We get rid of parentheses

48n^2+288n-2n+7=0

We add all the numbers together, and all the variables

48n^2+286n+7=0

a = 48; b = 286; c = +7;
Δ = b2-4ac
Δ = 2862-4·48·7
Δ = 80452
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:

$\sqrt{\Delta}=\sqrt{80452}=\sqrt{4*20113}=\sqrt{4}*\sqrt{20113}=2\sqrt{20113}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(286)-2\sqrt{20113}}{2*48}=\frac{-286-2\sqrt{20113}}{96}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(286)+2\sqrt{20113}}{2*48}=\frac{-286+2\sqrt{20113}}{96}
$