Alienware ax51 gpu upgrade

Hi everyone. I'd like to update my gpu to a nvidia gtx 970 but before doing any purchase i want to know if the new video card will work.

My current alienware is this:

AX51 I781TBW8S

It came with a 330w PS.

I was thinking about this one in particular:

EVGA NVIDIA GeForce GTX 970 Superclocked, 4 GB GDDR5, DisplayPort, HDMI, DVI, PCI Express x16 3.0

Do you think it will work?

Thanks in advantage.