Y4-17y2=-16

Solution for Y4-17y2=-16 equation:

4-17Y^2=-16

We move all terms to the left:

4-17Y^2-(-16)=0

We add all the numbers together, and all the variables

-17Y^2+20=0

a = -17; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-17)·20
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{85}}{2*-17}=\frac{0-4\sqrt{85}}{-34}
=-\frac{4\sqrt{85}}{-34}
=-\frac{2\sqrt{85}}{-17}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{85}}{2*-17}=\frac{0+4\sqrt{85}}{-34}
=\frac{4\sqrt{85}}{-34}
=\frac{2\sqrt{85}}{-17}
$