I need to solve an expression located at www.merelis.com for r. 
Everything else there is a constant.

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Request for Question Clarification by websearcher-ga on 28 Feb 2005 12:09 PST

Hello peter_nyc:

Are you interested in the steps to solve this or in just the final solution?

websearcher

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Clarification of Question by peter_nyc-ga on 28 Feb 2005 12:20 PST

Well, I suppose the method would be of most interest.  I'm also
wondering whether the solution can be simplified to some extent.

By cross-multiplying and solving, we can get a quadratic in r and use
the quadratic formula. Explicitly: (I'll use "b" for beta and "d" for
delta -- watch parentheses for order of operations):

Set x = (-(1/4)*b*[b - d + d' - b' - a]) + ((1/4)*b*[(1/2)*b - (1/2)*b' + d - d'])

Set y = ((1/2)*b*[b - d + d' - b' - a]) - (a*[(1/2)*b - (1/2)*b' + d - d'])

and set z = a - b + d - d'.

Hopefully I haven't made any transcription mistakes. Now, by the
quadratic formula, you will get two answers:

1) (-y + sqrt{y^2 - 4*x*z})/(2*x)

and

2) (-y - sqrt{y^2 - 4*x*z})/(2*x).

These are the solutions for r. Depending on the values of your
constants, the value under the radical could be negative, in which
case you'll get complex answers for r instead of real answers.