Will it fit in my motherboard or will I bet wasting my money? If it won't fit can someone recommend me a card that will run Tera with good graphical settings, I have a 1080p 32inch HD screen TV for as my monitor.
check the length of the gpu you want in its specs which is 241mm so your gonna want about 10" clearance then measure the clearance you have inside the case ( so it isnt gonna hit the drive bays or anything like that), also your gonna need the slot below the pci-e clear as that gpu is dual slot (double height) i would also be very concerned about your psu, i would seriously recommend replacing your existing one if its not around 450watt in a respectable brand which is also going to need a 6pin gpu power connectors
going through the manual pics looks like only issues u could have is clearing the hard drive cage towards the end of the evga card and that small heatsink below the pci slot , i don't think you should have any hassles as it looks like its not that high
if you have something plugged into the top one of the the two small slots ( #17) you would need to drop in down a slot as the new card will be double the width of you current card
it could be a tight fit with the ram slots (#3) , those end clip-in's need some room to open , so u might have to remove the card at some point if you wish to replace the ram at any point , as shown http://www.manualslib.com/manual/1221/Acer-Aspire-M3910...
the sata ports ( #7 ) should have no clearance issues
as jason said you might want to upgrade the power supply also to something newer