I just bought a case with a 20 pins socket psu, my motherboard requires a 24 pins socket. I just found a 20 to 24 pin adaptator on a random web site. Is it ok to use those kind of adaptator without having to buy a new motherboard after plugging the psu?
Why not? It will definitely work fine and you cannot go wrong really. There is no need to buy a new motherboard when in fact most new motherboards are 24pin
If anything you would want a new PSU, not a new mothboard, the PSU you got is prabally crappy anyywas's, msot that come with case's are. But the adapter should work fine.
If it has enough power on the +12V rail, then it should be fine with just the 20-pin, but a 24pin has 2x +12V rails, so it has much more power. If you dont want to get a new PSU then i would buy that adapter.
You may be getting something you don't need. What is your set up ?
If you are using a Mobo that has video and thats the way you set up your system then you don't need the 24 pins. The extra 4 pins are for you PCI-X.