Troubleshooting Rearranging Equations: How to Solve for v in a Complex Equation

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The discussion centers on the difficulty of rearranging the equation P=[RT/(v-b)]-[a/v(v+b)T^0.5] to solve for v. The original poster expresses frustration after spending an hour attempting to manipulate the equation without success. Participants point out the ambiguity in the equation's formatting, suggesting multiple interpretations that could affect the solution process. Clarification is requested to determine whether the question is intended for a math or engineering context. Clear communication of the equation is essential for effective troubleshooting and assistance.
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Alright I'm going absolutely nuts here. It's a simple matter of rearranging an equation and for the life of me I can't do it. I've been working at it for like an hour now to no avail. Here's the equation.

P=[RT/(v-b)]-[a/v(v+b)T^0.5]

I'm trying to solve for v. I've manipulated this equation every way I can think of and still can't get it. I'm sure it's something simple but I'm stuck. Please help.
Thanks
 
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Can you put either put redundant parenthesis around everything or put the equation in LaTeX format (tutorial is in the general physics stickies)?
 
eric99gt said:
P=[RT/(v-b)]-[a/v(v+b)T^0.5]
As enigma suggests, there is quite a bit of ambiguity in how you wrote your equation. Here are a few of the possible ways we could interpret what you wrote.

The first part of your equation could be R[T/(v-b)] or (RT)/(v-b)
The second part could be
[(a/v)(v+b)(T^.5)] or
{[a/(v(v+b))](T^0.5)} or
{(a/[v(v+b)(T^0.5)]}

Can you clarify?
 
Your question appears the same as the one you posted on engineering homework: query.
Did you mean to post it as a math question or engineering?
 
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I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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