Solving an equation with an unknown in the numerator and denominator

Hello,

I'm trying to solve this equation for M (shown below), everything is unknown besides M. I tried using the solve function however it returned an implicit solution. Is there any way I can solve this equation to return an explicit value?

Here's the ouput:

Thanks in advance

syms M positive
  A = (k+1)/(2*(k-1));
  D= k-1;
  E= k+1;
  
  syms s;
  
  eqn = (1/M)*((2+(D*M^2))/(E))^A == 3.5;
  S=solve(eqn, M,'MaxDegree',3)
 

Answer 1

[Stephan]

syms M k

A = (k+1)/(2*(k-1));
D =  k-1;
E =  k+1;

eqn = (1/M)*((2+(D*M^2))/(E))^A == 3.5;
sol = vpasolve(eqn);

pretty(eqn)
M_sol = sol.M
k_sol = sol.k

test = subs(eqn,[M,k],[M_sol,k_sol])