"Cheap" - what is your definition?
Get the power brick for your laptop, and see the details, it probably reads "65W, 19V". It will need twelve hours to fill in one KWh, which your utility sells you for like $.20, so we have the base - twenty cents for twelve hours (make it a day).
Now, you need a solar panel which can give 65watts on 19Volts. The closest match
here is little bit over $100.
So, your investment of $100 will get break even after five hundred days - each of them with 12 hours of sun. Go figure whether it is worth.
Don't take me wrong - I am all about renewable energy. But in order to make a saving, you need an investment of several thousand dollars, not one Benjamin.