I studied about the Laplacian at https://www.youtube.com/watch?v=EW08rD-GFh0 and I understand that it can be thought of as the second order derivative test where the value $ \triangle f(x,y) $ will be high at a local minima and low at a local maxima.
But what does it mean to solve for the laplacian i.e. $ \triangle f(x,y) = 0$ ? I have extremely little background in physics so it would be nice if someone, bearing that it mind, explain what it means to solve for the laplacian. I come from an image processing background and have only used the laplacian operator for edge detection so "solving" it sounds completely alien to me.