# Help me solve this equation; I believe this is a transcendental equation [duplicate]

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.

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

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• 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. – bbgodfrey Oct 7 '15 at 1:15

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  *)

• You can also do N[Reduce[{eqn,0<=x<=140},x]]. – Jens Oct 7 '15 at 4:01