TV mount on wooden studs - what screws to use
I agree with unhandledexcepsean--I would use lag bolts for larger TVs. Some flat screens will be fine with the wood screws through the drywall into the stud not using the plastic expanding anchor. I have seen some smaller mounts where 4 of the plastic anchors into drywall are supposed to work but I do not like those at all. 

Since you have at least 1 stud, measure 3/4” from 1 edge and mark. This will be the center of a two-by. If doubled two-bys then 16” over and there should be another stud. If not check the other side of the 3” stud measure in 3/4” mark (1-1/2” between marks) and see if there is a stud there. 16” on center is a most common spacing and if a wide bracket it should be set up for 16, 32, 48” widths.