your ENTIRE question hinge on information you are vague on. WHICH delta fans are you using EXACTLY,(model number) i've seen delta fans ranging from 4 watts to 84 watts EACH. that makes a HUGE difference in what we would recommend as solution.
generally speaking, if you NEED more then a high quality 1200w PSU, you are either doing it wrong or are playing with sub ambient cooling
just a quick power calculation, 4 x titans (4x250w) + 3970x (150w) = 1150w total draw. + overhead will push you over the 1200w budget, HOWEVER, the chances of you actually drawing that much even under stable OC is unlikely at gaming loads. SLi doesn't burn each card to 100% no matter how good the driver is or how optimized the game is.
IF you are building a F@H rig with 4 titans then sure, i'd strongly recommend a 1300w to 1500w like everyone else is recommending. but you really should ask yourself, WHAT exactly are you getting out of that 4th titan? 3 titan is about the limit as to what you can effectively use. that 4th titan is just a waste of money...