n(n+4)=221

Solution for n(n+4)=221 equation:

n(n+4)=221

We move all terms to the left:

n(n+4)-(221)=0

We multiply parentheses

n^2+4n-221=0

a = 1; b = 4; c = -221;
Δ = b2-4ac
Δ = 42-4·1·(-221)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-30}{2*1}=\frac{-34}{2}
=-17
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+30}{2*1}=\frac{26}{2}
=13
$