Y4+4y2-117=0

Solution for Y4+4y2-117=0 equation:

4+4Y^2-117=0

We add all the numbers together, and all the variables

4Y^2-113=0

a = 4; b = 0; c = -113;
Δ = b2-4ac
Δ = 02-4·4·(-113)
Δ = 1808
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1808}=\sqrt{16*113}=\sqrt{16}*\sqrt{113}=4\sqrt{113}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{113}}{2*4}=\frac{0-4\sqrt{113}}{8}
=-\frac{4\sqrt{113}}{8}
=-\frac{\sqrt{113}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{113}}{2*4}=\frac{0+4\sqrt{113}}{8}
=\frac{4\sqrt{113}}{8}
=\frac{\sqrt{113}}{2}
$