6n^2-32=-10

Solution for 6n^2-32=-10 equation:

6n^2-32=-10

We move all terms to the left:

6n^2-32-(-10)=0

We add all the numbers together, and all the variables

6n^2-22=0

a = 6; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·6·(-22)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{33}}{2*6}=\frac{0-4\sqrt{33}}{12}
=-\frac{4\sqrt{33}}{12}
=-\frac{\sqrt{33}}{3}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{33}}{2*6}=\frac{0+4\sqrt{33}}{12}
=\frac{4\sqrt{33}}{12}
=\frac{\sqrt{33}}{3}
$