The case is from the dell inspiron 3847-3850BK. The PSU is... http://www.corsair.com/en-us/cs-series-modular-cs450m-450-watt-80-plus-gold-certified-psu. and the motherboard is a 088dt1
Please just open the side window and measure how much space you have roughly where the gpu will go. Compare it with the dimension(s) of the card you are purchasing. Only doing this will give you 100% certainty.