Amplifier and superposition theorem

Hello All

I have a few sensors whose outputs are +- 5V, +-10V and +-20V.

I need to have a circuit which will have these signals changed to 0-5V range so that it can be connected to the ADC.

for example: if i consider +-10V sensor, i should get output as follows.
+10 V --> 5V,
0V --> 2.5V
-10V --> 0V,


I got a circuit that should reasonably do the same but i am unable to understand how the final function has been derived.

I have attached the circuit and final formula. If anyone can help me understand how the final formula has been reached, it would be of great help. I understand that super position theorem has been used to reach upto the final point. I am somehow not able to get how it is done.

Regards
Sachin

The circuit you posted is for a differential source. Are your sensors differential, or can one end of each be tied to the ADC's ground potential?