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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

6n^2-36n-24=0

a = 6; b = -36; c = -24;
Δ = b2-4ac
Δ = -362-4·6·(-24)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{13}}{2*6}=\frac{36-12\sqrt{13}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{13}}{2*6}=\frac{36+12\sqrt{13}}{12}
$