Ok,
So I took a look at the X51 R2 and, wow, that's a very unique design for the gpu alignment. Your power supply can definitely support the 970, your motherboard can definitely support the 970, the last thing is checking if your case can.
Take measurements of how long the gpu can be without hitting anything in your case. If the dimensions listed on the web are within what you measure, you're all set!
Since the X51 R2 is so compressed though, I would recommend purchasing a card with a 2-fan system instead of the 3 fans of the Gigabyte Windforce so that it will fit in your case. This one, for instance, by EVGA is every bit as powerful while being more conservative with space an energy.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121899
Hope that helps!