6-2n^2=-32

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

6-2n^2=-32

We move all terms to the left:

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

We add all the numbers together, and all the variables

-2n^2+38=0

a = -2; b = 0; c = +38;
Δ = b2-4ac
Δ = 02-4·(-2)·38
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{19}}{2*-2}=\frac{0-4\sqrt{19}}{-4}
=-\frac{4\sqrt{19}}{-4}
=-\frac{\sqrt{19}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{19}}{2*-2}=\frac{0+4\sqrt{19}}{-4}
=\frac{4\sqrt{19}}{-4}
=\frac{\sqrt{19}}{-1}
$