How do I express this equation in terms of Y?

This will become a quadratic equation once you clear Y from the denominator of the rightmost fraction. You can solve it using the quadratic formula.

I’m afraid, @IchtheosaurusRex , that your answer leaves me none the wiser

@meiosis , is this a homework-type question?

You need to simplify the equation so you have Y by itself in terms of X and the constants. First, you need to multiply out the expression in the denominator to clear the parentheses. Then you need to get Y out of the denominator.

“Expressing it in terms of Y” simply means to get Y by itself. It will probably be easiest to see if you begin by simplifying the denominator (the denominator is the bottom portion of a fraction).

Your denominator is: 500 * (500 / Y)
That’s the same thing as: (500 * 500) / Y = 250,000/Y

Now you have:
X = Y / (250,000 / Y)
Of course, you know how to divide fractions, so you recognize that this is the same thing as:
X = Y * (Y / 250,000)

Can you see what to do from here? (Even if not, you need to try to figure it out, and we will talk through your thought process. I’m not going to simply give you the answer.)

Wolfram alpha is good when you get stuck on things like this, but remember that you need to understand how you got there, which @bobbinhood gave a good explanation of:

http://www.wolframalpha.com/input/?i=X+%3D+(Y+/+(500+*+(500+/+Y)))

Thanks, I’ve got it sorted now. It wasn’t for homework, but for work. I have a slider on a web form that allows the user to specify the diameter of a circle, and I changed the way it works to allow for a greater degree of accuracy at the lower end of the slider, and needed to calculate a conversion process to change the old values to the new whilst retaining the underlying circle dimensions. I was having a Friday afternoon brain freeze, and you’ve helped warm it up for me…

Thanks again

School kids often ask, “Of what use is algebra in everyday life—why should I learn this stuff?”. @meiosis provides a perfect example. You never know when you’ll need to use your math skills.

@meiosis WolframAlpha has gotten me out of several programming jams where I have some bizzare conversion factor from x to y that I then need to resolve in terms of the opposite. Especially when dealing in high level trig.