Will Sapphire AMD Radeon R9 270X work in my X51?

I have an alienware X51 R2, with a GTX 645 graphics card in it and I have decided that I want to upgrade the GPU, I've looked around and it seems that the R9 270X is the best card to install, however this is my first time installing a graphics card an I have never bought one before. Could you tell me if this: http://www.amazon.co.uk/gp/product/B00FL8H49Q/ref=s9_simh_gw_p147_d0_i1?pf_rd_m=A3P5ROKL5A1OLE&pf_rd_s=center-2&pf_rd_r=1P0B2Y8A4BM7THQTP059&pf_rd_t=101&pf_rd_p=455344027&pf_rd_i=468294 

is compatible with an alienware x51 with the following specs:

PROCESSOR Intel Core i5-4430 (6MB Cache, up to 3.2GHz with Turbo Boost Technology)
OPERATING SYSTEM Windows 8 64bit, English
GRAPHICS CARD 1GB GDDR5 NVIDIA® GeForce® GTX 645
MEMORY 8GB Dual Channel DDR3 at 1600Mhz
HARD DRIVE 1TB (64MB Cache) 7200 RPM SATA 3Gb/s
OPTICAL DRIVE Slot-Loading Dual Layer DVD Burner (DVD RW, CD-RW)
WIRELESS CONNECTIVITY DW1506 Wireless-N WLAN Half Mini-Card

PSU 330 Watts