How to derive the transfer function of the Inverting Summing Amplifier?
For anyone interested how I derived the transfer function, here is the solution:

(This is the derivation for the schematic as shown in the question. If you have more inputs, just do the same procedure for each one.)



So, the solution was to have as many transfer functions as your inputs, and then the derivation is the same as an Inverting Amplifier.