3n(2+n)=6

Solution for 3n(2+n)=6 equation:

3n(2+n)=6

We move all terms to the left:

3n(2+n)-(6)=0

We add all the numbers together, and all the variables

3n(n+2)-6=0

We multiply parentheses

3n^2+6n-6=0

a = 3; b = 6; c = -6;
Δ = b2-4ac
Δ = 62-4·3·(-6)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{3}}{2*3}=\frac{-6-6\sqrt{3}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{3}}{2*3}=\frac{-6+6\sqrt{3}}{6}
$