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I'm working on an equation like :

a.sin(x(1+k))+b.sin(x(1-k))-c.sin(x) = 0

where x is the variable and the others one (a,b,c,k) are constant.

I tried to solve it manually but I didn't find any simple solutions.

I tried to solve it using some softwares (Mathematica and Matlab) using solve, nsolve and dsolve but without success.

What's the best software and/or the best argument (xsolve) to use ?

I want to find the analytical solution or, if it's not possible, I would like to have 10 positive numerical solutions.

Thank you.

PS : For anyone interested, this equations is a prior to use an equation of diffusion in porous material.

a = 5,95E-01

b = 5,22E-02

c = -3,53E-01

k = 0,14

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# Solving Equation Sinus

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