-3n(n+6)=18

Solution for -3n(n+6)=18 equation:

-3n(n+6)=18

We move all terms to the left:

-3n(n+6)-(18)=0

We multiply parentheses

-3n^2-18n-18=0

a = -3; b = -18; c = -18;
Δ = b2-4ac
Δ = -182-4·(-3)·(-18)
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{-(-18)-6\sqrt{3}}{2*-3}=\frac{18-6\sqrt{3}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{3}}{2*-3}=\frac{18+6\sqrt{3}}{-6}
$