We have similar triangles so
12/x = (12+78)/(x+13)
We can skip some algebra by doing the ratio on the pieces. We'll show it works at the end.
12/x = 78/13
x = 12(13)/78 = 2
We check
12/2 = 6
(12+78)/(2+13) = 90/15 = 6, good
Answer: x=2
