The right information from the figure is:
AU = 20x + 108,
UB = 273,
BC = 703,
UV = 444,
AV = 372 and
AC = 589
The similarity of the two triangles leads to:
[AB] / [AC] = [AU] / [AV]
[AB] = [AU] + [UB] = 20x + 108 + 273 = 20x + 381
=> (20x + 381) / (589) = (20x + 108) / 372
Now you can solve for x.
(372)(20x + 381) = (20x + 108)(589)
=> 7440x + 141732 = 11780x + 63612
=> 11780x - 7440x = 141732 - 63612
=> 4340x = 78120
=> x = 18
Answer: x = 18