can i fit the EVGA GeForce GTX 960 FTW ACX 2.0+ into my alienware x51?

Depending or your PSU you may be better getting a R9 280x(faster than the 760 and 960) they are around the same price as the 960. The 280x is going to use more power so make sure your PSU is up to the task. To see if there is room in the case you'll need a ruler or tape measure, Dell doesn't list a max gpu length in the specs.