Operational Amplifier (op amp) with different in
Your circuit is an example of a summing amplifier.

You might find this resource useful for understanding more about them, and armed with the proper term, Google will be a good friend :)

Note that your \$V_{in}\$ will always be 0, unless you've driven the op amp into saturation somehow. Since the non-inverting (+) input is grounded, the inverting input becomes a so-called "virtual ground". So your equation is not correct for this configuration.

Your experimental results are in the right direction. I think you'll find that the proportion of \$R_3\$ to \$R_1\$ and \$R_2\$ determines a scaling factor for the output.