Hi, could I get some help with this micro/macro-connection physics problem involving diatomic gas thermal interaction?

The set up is:

For two diatomic gases thermally interacting as shown in Figure 20.12, with degrees of freedom f as in the attached table, what is the final temperature T_f in kelvin (K) to 4 digits of precision if the given inital temperatures are T_1i = 90 K, T_2i = 2200 K, and N₂ = N₁/5.8 exactly?