4n(n+2)=44

Solution for 4n(n+2)=44 equation:

4n(n+2)=44

We move all terms to the left:

4n(n+2)-(44)=0

We multiply parentheses

4n^2+8n-44=0

a = 4; b = 8; c = -44;
Δ = b2-4ac
Δ = 82-4·4·(-44)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{3}}{2*4}=\frac{-8-16\sqrt{3}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{3}}{2*4}=\frac{-8+16\sqrt{3}}{8}
$