According to the owner's manual your system can support up to 8gig of memory minus other devices witha 64 bit OS. 4 gig with a 32 bit os.
Your board contrary to this thread does have a x16 slot.
CAUTION: Before you perform any of the procedures in this section, follow the
safety instructions in the Product Information Guide.
NOTICE: To prevent static damage to components inside your computer, discharge
static electricity from your body before you touch any of your computer’s electronic
components. You can do so by touching an unpainted metal surface on the computer.
Your Dell™ computer provides the following slots for PCI and PCI Express cards:
• Three PCI card slots
• One PCI Express x1 card slot
• One PCI Express x16 card slot
• One PCI Express x8 card slot (electrically configured as an x4)
As long as you can confirm that with the odd layout/case setup that the card fits and that you have sufficent power the motherboard shouldn't limit you from putting in that card.
Edit to add: Dell lets you configure it with a 3870x2 so there should be enough space.