You may have to upgrade your power supply (PSU)
Many 6670's do not require power from your power supply, they get enough power from the PCIE slot.
The 7850 will require a power from a PCIE power connector from your power supply which will need to be in the 400+ watt range with about 10Amps extra available on the rail. If your PSU uses multiple rails 12v1 typically powers the CPU and 12v2 powers everything else. So if you have 1 rail you want it to have about 30+A available and if you have two you want about 15A or more on 12v2.