-51-11n=n^2+7n

Solution for -51-11n=n^2+7n equation:

-51-11n=n^2+7n

We move all terms to the left:

-51-11n-(n^2+7n)=0

We get rid of parentheses

-n^2-11n-7n-51=0

We add all the numbers together, and all the variables

-1n^2-18n-51=0

a = -1; b = -18; c = -51;
Δ = b2-4ac
Δ = -182-4·(-1)·(-51)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{30}}{2*-1}=\frac{18-2\sqrt{30}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{30}}{2*-1}=\frac{18+2\sqrt{30}}{-2}
$