6n^2-18n-18n=6

Solution for 6n^2-18n-18n=6 equation:

6n^2-18n-18n=6

We move all terms to the left:

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

We add all the numbers together, and all the variables

6n^2-36n-6=0

a = 6; b = -36; c = -6;
Δ = b2-4ac
Δ = -362-4·6·(-6)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{10}}{2*6}=\frac{36-12\sqrt{10}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{10}}{2*6}=\frac{36+12\sqrt{10}}{12}
$