Simple, you just need to buy a new PSU
Rogue Leader nailed it with "This has bad idea written all over it"
Bottom line if your how-ever-many watt PSU does not have 8 pin connector on it (or even 6 pin) then it is not actually designed to handle that GPU.
Which means it is either a good 300w unit that is designed for internet and ms office use but will never power a 280x.
Or it is a power supply shaped piece of garbage that has a large number printed on a sticker.
A quality PSU can sustain outputting its max load during peak use, and will last for many many years.
A junk garbage power supply can not handle outputting even half of the load printed on the sticker, and when it dies it will fry that new GPU of yours, and the motherboard and possibly the CPU as well.
So bottom line: you can wait off installing that new 280x until you can buy a new PSU, or you can ghetto-rig it and hope that you get a week or two of gaming out of it before that PSU kills $400 or more worth of parts.