I have had many students use desmos to self-check their work. One way in which they do this (and I stress that they do this AFTER they work out a mathematical thought) is to type each equation into desmos and check to see if the solution is the same each time. For example:
I'm not overly fond of this method because I want students to be able to develop their own self-checking abilities and not rely on someone or something to judge their work; however, I can see some value in this method providing scaffolding as students gain confidence in their own abilities.
Another way in which students use desmos to self-check is by graphing complicated equations to see if they match. For the same reasons, I see drawbacks, but some value in this as well. I think there is value in helping them find connections between graphs and equations. The example below shows how one student explored completing the square.
This led the student to wonder why the graphs didn't match. Eventually they figured out that they need a coefficient of one on the quadratic term before they can complete the square. Link
How do you use desmos?