Which version of CCC you've been trying to install? (latest beta 14.1?)
What do you mean by "not installing", did the installation fail?
- If this is the case, make sure you have downloaded the right version compatible to your 280x and your OS which is Windows 7 64-bit.
http://support.amd.com/en-us/download/desktop?os=Windows%207%20-%2064
Try reinstall CCC couple of times and reboot your computer if any errors occured during the installation. Extracted installer is located at C:\AMD (if I'm not mistaken).
Your PSU is fine and more than enoguht for that GPU.
Your GPU R9 280x is made by which manufacture? (Asus? Sapphire? Gigabyte? etc.) Make sure you have plugged in all required power slot on your GPU, for example 2x8 pin connectors for 280x Toxic.