How to seperate equation for making a program

'''
######################mathematica
mathematica, as I recall
NSolve[Log[w18] == (zr*s0)+9.36 * Log[sn + 1] - 0.2 + ((Log[psi/(4.2-1.5)])/(0.4+(1094/(sn+1)^5.19)))+2.32*Log[mr]-8.07/.{zr->1,s0->2,psi->3,mr->4,w18->5},sn]
'''

#########################python:

from numpy import newtonsMethod # this statement is intended only to give the gist of the idea.

import math

class PVT:

    def __init__(self,zr,s0,psi,mr,w18):
        (self.zr,self.s0,self.psi,self.mr,self.w18) = (zr,s0,psi,mr,w18)
        self.max = 999

    def __call__(self,sn):
        (zr,s0,psi,mr,w18) = (self.zr,self.s0,self.psi,self.mr,self.w18)
        log = math.log
        try:
            zero = (zr*s0)+9.36 * log(sn + 1) - 0.2 + ((log(psi/(4.2-1.5)))/(0.4+(1094/(sn+1)**5.19)))+2.32*log(mr)-8.07-log(w18)
        except:
            zero = self.max
        self.max = max(zero,self.max)     # prepare for bad values
        return zero


# again, this statement is only approximately correct
print(newtonsMethod(function=PVT(zr=1,s0=2,psi=3,mr=4,w18=5),initialGuess=6))


'''
############################### j
NB. www.jsoftware.com  you'll need to install the addons.

require'~addons/math/misc/amoeba.ijs'

Sn=: adverb define
 'zr s0 psi mr w18' =. m
 sn=. y
 t0=. zr*s0
 t1=. 9.36*^.>:sn
 t2=. _0.2
 n=. ^.psi%4.2-1.5
 d=. 0.4+1094%(>:sn)^5.19
 t3=. n%d
 t4=. 2.32*^.mr
 t5=. _8.07
 t6=. -^.w18
 terms=. t0,t1,t2,t3,t4,t5,t6
 +/terms
)


Note 'Example'
   To the best of my understanding, this does solve the example
   of page 8, Topic 7 - AASHTO Flexible Pavement Design.pdf

   With zr = 0.91, s0 = 0.35, psi = 2, mr = 5, and w18 = 5e6

   amoeba is an optimizer,
   0.91 0.35 2 5 5e6 Sn  is the verb to zero
   hence we square it.  *:
   1e_4 is the tolerance,
   5,:6 is the starting simplex


   (*:@:(0.91 0.35 2 5 5e6 Sn)) (amoeba 1e_4) 5,:6
┌───────┬──────────┐
│5.08594│7.51186e_9│
└───────┴──────────┘
)

'''

# scipy comes from www.scipy.org

import math
import scipy  # also has log
import scipy.optimize

class PVT:

    def __init__(self,zr,s0,psi,mr,w18):
        (self.zr,self.s0,self.psi,self.mr,self.w18) = (zr,s0,psi,mr,w18)
        self.max = 999

    def __call__(self,sn):
        (zr,s0,psi,mr,w18) = (self.zr,self.s0,self.psi,self.mr,self.w18)
        log = math.log
        try:
            n = log(psi/(4.2-1.5))
            d = 0.4+(1094/((sn+1)**5.19))
            fraction = n/d
            zero = (zr*s0)+9.36*log(sn+1)+(-0.2)+fraction+2.32*log(mr)-8.07-log(w18)
        except:
            zero = self.max
        self.max = max(zero,self.max)     # prepare for bad values
        return zero

def minimize_me(**kwargs):
    f = PVT(**kwargs)
    return lambda sn, f = f : f(sn)**2

func = minimize_me(zr = 0.91, s0 = 0.35, psi = 2, mr = 5, w18 = 5e6)

amoeba_solution = 5.086
print(scipy.optimize.fmin_bfgs(func,amoeba_solution,full_output=True))

def f(x):
    return (4*x+2)**2

print(scipy.optimize.fmin_bfgs(f,0))