(0.42*x+0.78*1 2/3)*1 4/9 / 0.6-0.5*5 2/3=0.5

   =(91/150 х +1 79/90) / (-1 7/30)=0,5

1)   0,42х * 1 4/9=21/50 х * 13/9=91/150 х
2)   0,78 * 1 2/3 * 1 4/9=39/50 * 5/3 * 13/9=169/90=1 79/90
3)   0,5*5 2/3=1/2 * 17/3=17/6=2 5/6
4)   0,6 - 2 5/6=3/5 - 2 5/6=18/30 - 2 25/30= - 1 7/30

решаем дальше уравнение

91/150 х+1 79/90=0,5*( -1 7/30)
91/150 х+1 79/90= - 1/2 * 37/30
91/150 х= - 1 79/90-37/60
91/150 х= - 1 158/180-111/180
91/150 х= - 1 269/180= - 2 89/180
х= - 2 89/180 : 91/150
х= - 449/180 * 150/91
х= - 8 61/273