title: Solve an implicit function
body: <p>I have an implicit function to solve:</p>
  
  <p><a href="https://i.stack.imgur.com/fPtDj.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/fPtDj.png" alt="enter image description here"></a></p>
  
  <p>So I tried root finding functions from scipy.optimize:</p>
  
  <pre><code>- fsolve : RuntimeWarning: The iteration is not making good progress, as 
    measured by the improvement from the last ten iterations.
  - excitingmixing : NoConvergence
  -brent:  RuntimeWarning: invalid value encountered in double_scalars (but 
    without a chance to set constraints)
  </code></pre>
  
  <p>I have to confess that I'm not sure about the correct solver. Could someone please help?</p>
  
  <p>Minimal working example:</p>
  
  <pre><code>from scipy.optimize import fsolve, newton, brent, excitingmixing
  import numpy as np
  
  def func_zeta(zeta):
      k= 1.2
      Re = 5000.
      d = 0.03
      return (2.51 /Re/np.sqrt(zeta)+k/d/3.71) + 10**(0.5/ np.sqrt(zeta))
  zeta = fsolve(func_zeta, 64/Re)
  </code></pre>