Are you good at manipulation?

Write $(a,b,c,d) = (a,a+x,a+y,a+x+y)$ . Then $93 = bc-ad = xy$ . So there are two cases: $x = 1, y = 93$ , or $x=3, y = 31$ .

There are 405 tuples in the first case, from $(1,2,94,95)$ to $(405,406,498,499)$ , and 465 tuples in the second case, from $(1,4,32,35)$ to $(465,468,496,499)$ . So the total is $\fbox{870}$ .