I have the same board as you, it's an Acer RS780HVF. AM3 has a different amount of sockets and contacts than AM2+ I think, but an AM3 CPU may work. You should send AMD or Acer an email enquiring about this.
I found this, hopefully it's of relevance; AM3 processors are backwards-compatible with Socket AM2+, contingent upon a BIOS update for the motherboard. Manufacturers including Asus, Gigabyte, and others have labeled existing AM2/AM2+ boards as being "AM3 Ready" or similar, indicating that BIOS support is provided for the specified boards. This allows existing AM2/AM2+ systems to upgrade the CPU without having to upgrade any other components.