It's only a dual core. I couldn't find a quad core on newegg, but I believe the Intel Core 2 Quad Q8400 is a 775 socket, which is for a ddr2 mobo. You should figure out the socket of your motherboard though.
Ignore Spray honestly speaking man you can just sink less than 100 USD into a mobo. I got myself an MSI 870 g45 and its running a quad core. The processor tho is whats going to cost you. And put what type of MOBO you actually have to we can bring you more information.