6n^2+18n=108

Solution for 6n^2+18n=108 equation:

6n^2+18n=108

We move all terms to the left:

6n^2+18n-(108)=0

a = 6; b = 18; c = -108;
Δ = b2-4ac
Δ = 182-4·6·(-108)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-54}{2*6}=\frac{-72}{12}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+54}{2*6}=\frac{36}{12}
=3
$