Unable to find explicit solution

I have MATLAB R2020a and need to solve the equation below:

syms x P R F A
eqn = (F^2*P^(R - 1)*x)/(2*(x^R - P^R + P^R*R))==A 
S = solve(eqn,x)

But I receive this:

Warning: Unable to find explicit solution. For options, see help. 
> In sym/solve (line 317) 
 
S =
 
Empty sym: 0-by-1

Is there anyway to solve that equation or any idea?

[David Goodmanson]

Hi S^2,

the eqn is going to reduce to

c3*x^R + c2*x + c1 = 0

where the c's are constants, and for arbitrary R there is no analytic solution for this. Numerically, yes.

[SooShiant]

How to solve that equation numerically? I am new to MATLAB. May you write the code?

[David Goodmanson]

see 'doc fzero' for some examples of setting up a function of x and finding out when it is zero. All the constants have to be numerical, and take the denominator over to the other side, so that the function to find the zero of is going to be

(F^2*P^(R - 1)*x)  -A*(2*(x^R - P^R + P^R*R)) 

[SooShiant]

Great, You Are Genius. How to add a reputation for you?

[David Goodmanson]

Hi S^2, thanks for the thought, but you can't add reputation points because I posted it as a comment and not an answer, besides which what I said did not tell the whole story. fzero will also work on

(F^2*P^(R - 1)*x)/(2*(x^R - P^R + P^R*R)) - A 

which is closer to the original eqn. With that you just have to be a bit more careful with a starting guess region, because the denominator can go to zero (depending on the constants), sending the function to infinity.