n(5+n)=165

Solution for n(5+n)=165 equation:

n(5+n)=165

We move all terms to the left:

n(5+n)-(165)=0

We add all the numbers together, and all the variables

n(n+5)-165=0

We multiply parentheses

n^2+5n-165=0

a = 1; b = 5; c = -165;
Δ = b2-4ac
Δ = 52-4·1·(-165)
Δ = 685
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{685}}{2*1}=\frac{-5-\sqrt{685}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{685}}{2*1}=\frac{-5+\sqrt{685}}{2}
$