Solving a bizzare equation

[avci]

Can anyone help me solve this equation? I tried everything but couldn't manage it. 

[VladimirN]

Please attach your Mathcad worksheet (in archive file format) to the message.

[avci]

Here it is.

Thanks in advance.

[Werner_E · Accepted solution]

Why not use a numeric solve block?

But your function is rather beasty, being very steep and so guess value and value for CTOL are important.

Furthermore you'll notice that with th standard CTOL of  10^-3 the result is not excat (CM(R.0) != 0)

Also the used algorithm counts - only Levenberg-Marquardt will find a ssolution, Conjugate Gradient and Quasi-Newton won't.

[avci]

I also tried numerical solve block but it didnt work as well. The main problem with my code, I believe, was the initial guess as you suggested. I have never thought it would be that sensitive. I noticed the solution is not exact but exact enough since safety factor of 4.2 is already set. 

Thanks for your help.