The answer, as usual, is it depends.
Location is a big factor... It would obviously be cheaper to open a practice in a rural community than on 5th Avenue in Midtown Manhattan.
Equipment can range from frugal, such as second-hand chairs, to the latest stuff from Sirona that costs an arm and a leg. If you are a specialist, equipment cost will also vary as you purchase stuff particular to your specialty (for example, surgical microscopes for endodontists).
How large is the office plays a factor too-- It affects the amount you have to outlay for the equipment.
I've seen numbers ranging from $150,000 to $1 million to open a new dental practice..