8=(-19-7n)n+7

Solution for 8=(-19-7n)n+7 equation:

8=(-19-7n)n+7

We move all terms to the left:

8-((-19-7n)n+7)=0

We add all the numbers together, and all the variables

-((-7n-19)n+7)+8=0


We calculate terms in parentheses: -((-7n-19)n+7), so:

(-7n-19)n+7

We multiply parentheses

-7n^2-19n+7

Back to the equation:

-(-7n^2-19n+7)


We get rid of parentheses

7n^2+19n-7+8=0

We add all the numbers together, and all the variables

7n^2+19n+1=0

a = 7; b = 19; c = +1;
Δ = b2-4ac
Δ = 192-4·7·1
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-3\sqrt{37}}{2*7}=\frac{-19-3\sqrt{37}}{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+3\sqrt{37}}{2*7}=\frac{-19+3\sqrt{37}}{14}
$