Solving for degeneracy electron cloud temperature

[kamui1]

Homework Statement:

Assume degeneracy starts to dominate approximately when the pressure expected from a completely degenerate electron gas equals that expected from an ideal gas (P_rel_e=P_ideal=1/2Ptotal) Show that the temperature at that point, which we assume will be the maximum reached, is given by T_max is true

Relevant Equations:

Tmax= 7.7x10^7 K mu*mu_e^5/3*(M/M_solar)^5/3
P_rel_e = K(ro/mu_e*m_h)^5/3
P_ideal = nKT

When I try P_rel_e = P_ideal I couldn't get a single number that is close to the given T_Max. It might be that I used the wrong equations but I am not sure. Can anyone give me some guidence on this question?