How to adjust parameter from equation based on desirable output?

Question

I am trying to adjust an specific value (di) based on equation (Arps - for decline curve analysis) so the sum of my original + predicted values (new_sum) match my reference value (sum_reference).

The original values:

df = pd.DataFrame({"YEAR":[2019, 2020, 2021, 2022, 2023],
                   "DATA":[0.5, 1, 2, 3, 4]})
df
Out[40]: 
   YEAR  DATA
0  2019   0.5
1  2020   1.0
2  2021   2.0
3  2022   3.0
4  2023   4.0

Some parameters I should use and then the decline equation:

sum_reference = 15  # the reference number I should have after the sum of original and predicted values
n_periods = 3  # number of years I should do my prediction for
qi = 4  # last data
di = 0.5  # temporary decline rate

# Equation
eq = qi / (1 + di * np.arange(1, n_periods + 1))
eq_df = pd.DataFrame({"YEAR":np.nan,
                      "DATA":eq},
                     index=np.arange(1, n_periods + 1))

# Adding new data to dataframe
df = pd.concat([df, eq_df])

df
Out[43]: 
     YEAR      DATA
0  2019.0  0.500000
1  2020.0  1.000000
2  2021.0  2.000000
3  2022.0  3.000000
4  2023.0  4.000000
1     NaN  2.666667
2     NaN  2.000000
3     NaN  1.600000

# New sum
new_sum = df["DATA"].sum()

When I look at the difference between the sums (sum_reference - new_sum), I get -1.766. Now I need to adjust my temporary decline rate "di" (automatically find a new number) so this sum difference be 0.

I was working on this problem in Excel and I could find this value while using Goal Seeker tool. But how I can use the same in Python? Or maybe another method?