5Y(4)-20y(2)=0

Solution for 5Y(4)-20y(2)=0 equation:

5(4)-20Y(2)=0

We add all the numbers together, and all the variables

-20Y^2+54=0

a = -20; b = 0; c = +54;
Δ = b2-4ac
Δ = 02-4·(-20)·54
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{30}}{2*-20}=\frac{0-12\sqrt{30}}{-40}
=-\frac{12\sqrt{30}}{-40}
=-\frac{3\sqrt{30}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{30}}{2*-20}=\frac{0+12\sqrt{30}}{-40}
=\frac{12\sqrt{30}}{-40}
=\frac{3\sqrt{30}}{-10}
$