How can I mount a desk on a wall with L-brackets?
L Brackets are not going to be a good idea for this type of project. As a minumum you will need to have a triangle type bracket - if you can find something large enough. If you want to avoid any type of legs right at the front edge you could build your own equivalent of a triangle bracket out of wood. 

If I was setting out to make a built in unit mounted onto a wall I would secure a wood piece along the wall to every stud at the table height minus the top thickness. Then I would use this horizontal strip as the rear side mount for the table top. Then I would install supports under the table from near the front edge and angle them down toward the bottom of the wall where they could be fastened into the wall stud and/or the floor.

At the end of the day I would really suggest that you step back and evaluate if it really necessary to fasten your table to the wall. Having it sit on its own supports makes for a huge bunch of flexibility. It can be moved, taken away when all computers of the future fit into a pocket and a computer desk is no longer needed, and lastly you can easily get it away if you ever want to sell the house.