How can i solve this equation with solve()

I want to solve this equation:

syms x

r = solve((0.02*(x-1)/(x^102 - 1))-7.59e-6,x,'ReturnConditions',true);
display(r.x)

ans = 

but the r.x field does not have a solution.

syms z

z = solve((0.02*(x-1)/(x^72 - 1))-7.59e-6,x,'ReturnConditions',true);

display(double(z.x))

   1.0766 + 0.0000i
   1.0795 - 0.1086i
   1.0795 + 0.1086i
   1.0724 - 0.2081i
   1.0724 + 0.2081i
   1.0545 - 0.3045i
   1.0545 + 0.3045i
   1.0270 - 0.3982i
   1.0270 + 0.3982i
   0.9905 - 0.4888i
   0.9905 + 0.4888i
   0.9458 - 0.5756i
   0.9458 + 0.5756i
   0.8932 - 0.6580i
   0.8932 + 0.6580i
   0.8332 - 0.7353i
   0.8332 + 0.7353i
   0.7664 - 0.8069i
   0.7664 + 0.8069i
   0.6934 - 0.8724i
   0.6934 + 0.8724i
   0.6148 - 0.9310i
   0.6148 + 0.9310i
   0.5312 - 0.9825i
   0.5312 + 0.9825i
   0.4432 - 1.0264i
   0.4432 + 1.0264i
   0.3516 - 1.0623i
   0.3516 + 1.0623i
   0.2571 - 1.0900i
   0.2571 + 1.0900i
   0.1605 - 1.1092i
   0.1605 + 1.1092i
   0.0625 - 1.1197i
   0.0625 + 1.1197i
  -0.0361 - 1.1216i
  -0.0361 + 1.1216i
  -0.1345 - 1.1147i
  -0.1345 + 1.1147i
  -0.2320 - 1.0992i
  -0.2320 + 1.0992i
  -0.3278 - 1.0751i
  -0.3278 + 1.0751i
  -0.4211 - 1.0426i
  -0.4211 + 1.0426i
  -0.5113 - 1.0020i
  -0.5113 + 1.0020i
  -0.5975 - 0.9535i
  -0.5975 + 0.9535i
  -0.6791 - 0.8977i
  -0.6791 + 0.8977i
  -0.7555 - 0.8348i
  -0.7555 + 0.8348i
  -0.8261 - 0.7654i
  -0.8261 + 0.7654i
  -0.8904 - 0.6901i
  -0.8904 + 0.6901i
  -0.9477 - 0.6094i
  -0.9477 + 0.6094i
  -0.9977 - 0.5239i
  -0.9977 + 0.5239i
  -1.0400 - 0.4343i
  -1.0400 + 0.4343i
  -1.0742 - 0.3414i
  -1.0742 + 0.3414i
  -1.1001 - 0.2458i
  -1.1001 + 0.2458i
  -1.1175 - 0.1482i
  -1.1175 + 0.1482i
  -1.1263 - 0.0495i
  -1.1263 + 0.0495i

When i change the exponent of x, i get a solution vector as i expect. I dont understand why this happens and how i can get a solution when r.x does not result in a solution vector.

Wolframalpha solution: https://www.wolframalpha.com/input?i2d=true&i=solve%5C%2840%29Divide%5B0.02*%5C%2840%29x-1%5C%2841%29%2CPower%5Bx%2C%5C%2840%29102-1%5C%2841%29%5D%5D-7.59e-6%5C%2841%29

Thanks for any help.

Answer 1

[Florian Bidaud]

You have the explanation here : https://uk.mathworks.com/matlabcentral/answers/512646-what-is-z1-appearing-when-solving-this-nonlinear-system-for-x-y-and-z

Solution could be using vpasolve :

syms x

r = vpasolve((0.02*(x-1)/(x^102 - 1))-7.59e-6,x);
display(r)

r = 

[Jean Volkmar]

Thank you very much :)