So I have this equation that’s great for finding one term. Problem is, I need to solve for another term that’s scattered all across the right side. I’m hoping someone here has the mad algebra skills I managed to lose in the two decades since I last took a math class and can help me out.
Here’s the original equation:
Q = (3.07 × F × Y × (1 + 1.4 × ((D/V) × e(-2 × D/V)))) / D2
I want to be able to solve for D, not Q; in other words, have a single D on the left and everything else on the right of the equation. F, Y, and V are all variable terms; the e is the classic irrational constant. I tried for quite a while to do this and ran very firmly aground. The best I managed was this minor simplification:
Q = (3.07 × F × Y × (1 + 1.4 × (D / (V × e(2 × D/V)))) / D2
…and even that assumes that I did things correctly. Here’s the original equation in pretty shoulda-done-it-in-MathML-but-oh-well form:
I can shuffle the chairs around, as it were, but never really get anywhere close to having a single D on the left. “But it’s so easy!“, you may well be shouting. That’s why you’re working for Google and I’m not.
I remember having questions just like this on tests back in college: “Given this equation, solve for blah”. It’s been too long, though, and in all honesty I was never that great at this sort of thing in the first place. Help, please?
[Update 14 Jan 09]: several commenters have shown that what I’m trying to do is impossible. Frustrating, but that’s math for you. Looks like I’ll have to take another approach.