I am trying to find the voltage at NODE1. My initial approach was to find the current starting from the \$15\$V source then going through \$R_1\$ and \$R_3\$ to ground. Then calculating the current from \$14\$V source through \$R_2\$ and \$R_3\$ to ground. Then adding the two currents and using Ohm's law with total current and \$R_3\$ to find voltage from NODE1 to ground. This seems plausible to me only because of KCL (total current entering a node must equal current exiting node). However my answer is incorrect as I have proved both in SPICE and on breadboard.
What am I missing? I would appreciate any suggestions that don't totally give me the answer.