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This question already has an answer here:

please can someone help me solve

 (x*L)+B*tan(x*L)=0, 

solve for x when B=10;L=0.1. The equation looks innocent but I need to find 1st 5 roots of equ.

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marked as duplicate by Jens, xyz, m_goldberg, Sjoerd C. de Vries, Kuba Oct 7 '15 at 6:47

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Welcome to Mathematica.SE! I hope you will become a regular contributor. To get started, 1) take the introductory tour now, 2) when you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge, 3) remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign, and 4) give help too, by answering questions in your areas of expertise. $\endgroup$ – bbgodfrey Oct 7 '15 at 1:09
  • $\begingroup$ Plot the function to see where the roots are, then use FindRoot to obtain the numerical values. The first is, of course, at 0. The second is at 28.6277. $\endgroup$ – bbgodfrey Oct 7 '15 at 1:15
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If you constrain the domain of x you can use NSolve

B = 10;
L = 1/10;

eqn = (x*L) + B*Tan[x*L] == 0;

soln = NSolve[{eqn, 0 <= x <= 140}, x, Reals, WorkingPrecision -> 10]

(*  {{x -> 0}, {x -> 28.62772588}, {x -> 57.60557933}, {x -> 
   87.08313831}, {x -> 117.0267808}}  *)

Verifying roots

And @@ (eqn /. soln)

(*  True  *)
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  • $\begingroup$ You can also do N[Reduce[{eqn,0<=x<=140},x]]. $\endgroup$ – Jens Oct 7 '15 at 4:01

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