Hi,
If the CPU doesn't appear on the support list then the answer is no, it won't work. However, having just had a look at a couple of the 770 & 785 series motherboards your CPU does seem to be supported. Don't forget that it is an AM2 CPU not an AM2+ so you have to check the right section.
If you could give the full name of the motherboard you are thinking of getting (for example GA-MA770-UD3 or GA-MA785GM-US2H) then it would be easy to say for sure if your CPU will run OK