You need some type of PWM or MPPT solar regulator ( maybe 10 A) hooked up to a battery ( maybe 30 Ah minimum, but it depends on usage) to keep powered-up predictably.
Next item is only around 4 USD:
To power my laptop on solar DC for the past 3 years I have been using a DC-DC step-up converter found on ebay. Search for:
DC converter 6-35V.
Look for the ones in the metal casing. You can pop the lids off these things easily, which is handy too. They are just held on by pressure of the side 'walls'. Anyway, an item like this will probably work well with most low to midrange laptops as long as your laptop doesn't sip too much power. Mine is low-end.
You will need to wire things up yourself. I think I am using 2.5mm squared wire which is just about the max those little terminals can take with ferrules on. I prefer to terminate the wires with ferrules for robustness and resistance to broken wire strands. Ferrules and ferrule crimpers are available online. I can't live without them.
The unit itself has a dial to adjust to your desired latop output voltage, so keep a multimeter handy. Also, every unit I've ordered has had mislabelled stampings on its metal case. Just pay more attention to the PCB markings than the case markings and you should be able to discern output from input.
On the laptop end you need the correct connector.
I normally buy something like this first:
5.5 mm x 2.1mm screw dc connector plug 10pcs
These plug in well to your final laptop plug, found with a search such as:
Universal laptop power adapter set 2.1mm
...on ebay.
With the suitable barrel connector and the suitable voltage via the step-up converter, you should be ready to go. No silly inverter needed.