Will a Gtx 970 fit inside a Dell Inspiron 3000 Series i3847-4617BK Desktop (3.2 GHz Intel Core i5-4460 Processor, 8GB DDR3, 1T

Solution
If you have that pc, open up the side panel. measure the space available where the graphic card will go (Usually the first pcie x16 slot).
Compare the result you got with the card's dimensions
EVGA GTX 970 ACX 2.0 dimension are:

Height: 4.376in - 111.15mm
Length: 9.5in - 241.3mm
If you have that pc, open up the side panel. measure the space available where the graphic card will go (Usually the first pcie x16 slot).
Compare the result you got with the card's dimensions
EVGA GTX 970 ACX 2.0 dimension are:

Height: 4.376in - 111.15mm
Length: 9.5in - 241.3mm
 
Solution
Also, I would recommend going with the newer variant of the ACX Superclocked 970 known as the SSC 2.0+ (model 04G-P4-3975-KR). I have two of them in SLI and they run cooler than the older ACX version as well as being more efficient (using less power). But it is very difficult if not impossible for anyone to tell if this card would fit inside that case. You'd have to take measurements from the PCIe slot like Suztera said. However that PSU is ATX and that is industry standard form factor of size, so it should fit (but knowing Dell like I know Dell and the upgradable friendliness, even that may be a tossup).