Like tkamiya says, it looks foggy anyway so it's probably not as bad as it looks. Which isn't to say that yours isn't grossly fogged. The usual recommendation with Delta-3200 (for any speed above 1000) is to develop it for the next stop higher EI, e.g. if you expose at 1600 then develop for 3200, etc.
Exposing at lower EI will get the image above the fog. You do lose a little dynamic range though because there's less density range available in the film to work with. 400 is pretty slow for that film and will result in really low-contrast negatives; I would have suggested 800. But then, you might need to shoot at 400 or even 200 because of the fog; we can't say without seeing how your first roll came out.
The presence of restrainers in a developer will reduce fog, as will the use of high-activity developers for short times that tend to work more on the highlights than shadows. HC-110 and Rodinal tend to give less base fog, but they also give poor film speed. They're a good choice if you have old film that you plan to over-expose.
You might find the FAQ link in my signature useful since you're newish to developing film.