Is this the series you are referring to?
http://www.dell.com/us/business/p/inspiron-3647-small-desktop/pd
If it is, the power supply (220W) will likely be insufficient for the GTX 960, especially if the card is custom or overclocked. Most reviews put system power at full load over 200W. Though the i3 and 8Gb of ram will cut down on your power consumption, the load will be very close to what your PSU is capable of delivering over its 12V rail. That is assuming it is capable of delivering the power it is rated for. The reference GTX 960 has a TDP of 120W.
Also, Dell has rocky support for the 900 series. You would also need to verify there is a BIOS update available that supports the 900 series.