# 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.

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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. Oct 7, 2015 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, 2015 at 4:01