A system with a GTX970 in it will need at least a
500W PSU and couple the fact that prebuilt system's don't come bundled with a quality/reliable unit. The PSU is also considered to be the heart of your system, if it has a heart attack, your entire investment can and will go down the drain, which is why I'm asking what your PSU's make and model is.
Can you take the side panel off and snap a pic of the sticker on the PSU? Would also be good to see how the ram slots are populated. You seem to be on the latest BIOS available off
Dell's support page.
I've also dug up some info about your motherboard:
http://www.technicke-specifikace.cz/cil/I3847.pdf
http://downloads.dell.com/manuals/all-products/esuprt_desktop/esuprt_inspiron_desktop/inspiron-3847-desktop_owner%27s%20manual_en-us.pdf
turns out you can max out your memory to 16GB. Being an H81 chipset, the effective frequency you can get out of DDR3 is 1600MHz. So in retrospect you can look forward to a DDR3-1600MHz 2x8GB 1.5v ram kit upgrade if you so wish.
That 200USD budget includes a PSU?