6-4n^2=-38

Solution for 6-4n^2=-38 equation:

6-4n^2=-38

We move all terms to the left:

6-4n^2-(-38)=0

We add all the numbers together, and all the variables

-4n^2+44=0

a = -4; b = 0; c = +44;
Δ = b2-4ac
Δ = 02-4·(-4)·44
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{11}}{2*-4}=\frac{0-8\sqrt{11}}{-8}
=-\frac{8\sqrt{11}}{-8}
=-\frac{\sqrt{11}}{-1}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{11}}{2*-4}=\frac{0+8\sqrt{11}}{-8}
=\frac{8\sqrt{11}}{-8}
=\frac{\sqrt{11}}{-1}
$