As Shayna mentioned, goldies and tetras need two different types of homes. I don't think you should ever see these two kinds of fish together in the same tank.

Goldies don't like their water nearly as warm as tetras
need theirs to be. Keeping your goldie at tropical temps like you see in a tetra tank will shorten your goldie's life considerably. So I agree, overstocking is not the only issue (though it is still definitely a concern).
From their profiles here on FishLore:
Bleeding Heart Tetra : 72°F - 80°F (22°C - 27°C) (
http://www.fishlore.com/profiles_ble...eart_tetra.htm)
Goldfish : 40°F - 80°F (5°C - 27°C) (
http://www.fishlore.com/Profiles-Goldfish.htm)
(Note: I would
never keep a goldfish at 80F except temporarily to treat illnesses such as ich and the like, but that IS the max temp listed there. My goldies were always kept right at room temperature [no heater], and they seemed happiest that way.)
I would either get rid of the tetra and keep the goldie (you may be able to return to the LFS?), or get rid of the goldie and get several more tetras for yours to school with. But I would not keep them both together, and I certainly would
not add any more fish to the tank as long as the goldfish was in there.
Sorry to be a party-pooper...

Hope this helps you decide, and good luck.
