two and a half digger

or, in the context of the task, I

published a habrozer here, and at some point in time I got a rating of 5. With a total of 12 votes :) The
subconscious, formed by a mathematical and technical education, began to rebel. I asked him what was the matter.
In general, if anyone finds a solution to the following system in whole numbers, there’s some kind of bonus :)
x + y = 12
xy = 5

It is clear that this is due to the fact that not all data is displayed on the page at one time. What do web programming experts say?

UPD: well, here again :)