Many different laptops can run multiple external monitors simultaneously; Apple is not the only company that sells computers with this capability. However, you will be very limited in your ability to run multiple external monitors from a computer that wasn't designed to.
In your case, the computer's specifications (assuming I found the right one) indicate that it has both a VGA and an HDMI output. If one of your monitors supports VGA and the other supports HDMI (or DVI, since it's easy to convert from HDMI to DVI), then you might be able to use two external monitors from your current laptop. It depends on the capabilities of the motherboard and graphics card. I've seen laptops that have the same GPU, where one can do 2 external monitors at once and the other can't, so it depends by driver and manufacturer.
Chances are that you will not be able to run both two external monitors and the built-in screen at the same time, so when configuring the monitor setup, keep that in mind. Give it a try with one on the VGA port and another on the HDMI port, and it might work!