6n^2-2n=330

Solution for 6n^2-2n=330 equation:

6n^2-2n=330

We move all terms to the left:

6n^2-2n-(330)=0

a = 6; b = -2; c = -330;
Δ = b2-4ac
Δ = -22-4·6·(-330)
Δ = 7924
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:

$\sqrt{\Delta}=\sqrt{7924}=\sqrt{4*1981}=\sqrt{4}*\sqrt{1981}=2\sqrt{1981}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{1981}}{2*6}=\frac{2-2\sqrt{1981}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{1981}}{2*6}=\frac{2+2\sqrt{1981}}{12}
$