How do I find the Thevenin voltage and resistance equations of this circuit?
The KVL in the center of the diagram should be a huge clue.

The Th&eacute;venin voltage is the open-circuit voltage. This is a moderately complex equation, but there's only one unknown: IR

You can easily get the short-circuit current by adding up the contributions of the two branches. Again, IR is the only unknown.

The Th&eacute;venin resistance is the ratio of those two results, by Ohm's Law.