-3n(n+6)+10=-8

Solution for -3n(n+6)+10=-8 equation:

-3n(n+6)+10=-8

We move all terms to the left:

-3n(n+6)+10-(-8)=0

We add all the numbers together, and all the variables

-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 = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{15}}{2*-3}=\frac{18-6\sqrt{15}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{15}}{2*-3}=\frac{18+6\sqrt{15}}{-6}
$