Chip for Chip
Is an Intel Core 2 Duo a plug in replacement for an Intel Core Duo? (Dell Inspiron E1750 laptop of 2006 build year)
It all depends on what motherboard is inside your laptop. You can find out easily enough by downloading a small free utility called "CPUZ" - run this and you will find out a whole load of information on your laptop regarding the CPU and mobo, along with RAM and chipset.
The motherboard tab should tell you the make and model - which you can check on the manufacturers website.
Now for the bad news. Upgrading anything other than the RAM and HDD on a laptop requires the case to be taken apart - which can be tricky even to the best of PC builders.
If you are feeling brave and can find a CPU to upgrade your laptop then I wish you good luck.