n(n+4)=117

Solution for n(n+4)=117 equation:

n(n+4)=117

We move all terms to the left:

n(n+4)-(117)=0

We multiply parentheses

n^2+4n-117=0

a = 1; b = 4; c = -117;
Δ = b2-4ac
Δ = 42-4·1·(-117)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-22}{2*1}=\frac{-26}{2}
=-13
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+22}{2*1}=\frac{18}{2}
=9
$