n(n+16)=-5

Solution for n(n+16)=-5 equation:

n(n+16)=-5

We move all terms to the left:

n(n+16)-(-5)=0

We add all the numbers together, and all the variables

n(n+16)+5=0

We multiply parentheses

n^2+16n+5=0

a = 1; b = 16; c = +5;
Δ = b2-4ac
Δ = 162-4·1·5
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{59}}{2*1}=\frac{-16-2\sqrt{59}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{59}}{2*1}=\frac{-16+2\sqrt{59}}{2}
$