5n+20-n(n+7)=-11

Solution for 5n+20-n(n+7)=-11 equation:

5n+20-n(n+7)=-11

We move all terms to the left:

5n+20-n(n+7)-(-11)=0

We add all the numbers together, and all the variables

5n-n(n+7)+31=0

We multiply parentheses

-n^2+5n-7n+31=0

We add all the numbers together, and all the variables

-1n^2-2n+31=0

a = -1; b = -2; c = +31;
Δ = b2-4ac
Δ = -22-4·(-1)·31
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8\sqrt{2}}{2*-1}=\frac{2-8\sqrt{2}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8\sqrt{2}}{2*-1}=\frac{2+8\sqrt{2}}{-2}
$