21Y=5(x)2

Solution for 21Y=5(x)2 equation:

21=5(Y)2

We move all terms to the left:

21-(5(Y)2)=0

determiningTheFunctionDomain
-5Y2+21=0

We add all the numbers together, and all the variables

-5Y^2+21=0

a = -5; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-5)·21
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{105}}{2*-5}=\frac{0-2\sqrt{105}}{-10}
=-\frac{2\sqrt{105}}{-10}
=-\frac{\sqrt{105}}{-5}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*-5}=\frac{0+2\sqrt{105}}{-10}
=\frac{2\sqrt{105}}{-10}
=\frac{\sqrt{105}}{-5}
$