sine rule

We can find angle BCA  in the large triangle thusly :

sin BCA / 5.6  =  sin 50  / 9.3

sin BCA  =  5.6sin 50  / 9.3

So

arcsin (5.6 sin 50 / 9.3)  = BCA  =  27.47°

So....in the smaller triangle BDC, angle BDC  is supplemental to angle BDA  =  180 - 78  = 102°

So  x  = angle DBC  =

180 - BDC - BCA  =

180  - 102 - 27.47  = 

50.53° =  50.5°