-6n^2=-330

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

-6n^2=-330

We move all terms to the left:

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

We add all the numbers together, and all the variables

-6n^2+330=0

a = -6; b = 0; c = +330;
Δ = b2-4ac
Δ = 02-4·(-6)·330
Δ = 7920
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:

$\sqrt{\Delta}=\sqrt{7920}=\sqrt{144*55}=\sqrt{144}*\sqrt{55}=12\sqrt{55}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{55}}{2*-6}=\frac{0-12\sqrt{55}}{-12}
=-\frac{12\sqrt{55}}{-12}
=-\frac{\sqrt{55}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{55}}{2*-6}=\frac{0+12\sqrt{55}}{-12}
=\frac{12\sqrt{55}}{-12}
=\frac{\sqrt{55}}{-1}
$