Answer :
[tex]19-\frac{5}{2x}=34\\\\\
-\frac{5}{2x}=34-19\\\\
-\frac{5}{2x}=15\ \ |*2x\\\\
-5=15*2x\\\\
-5=30x\ \ |:30\\\\x=-\frac{5}{30}=-\frac{1}{6}[/tex]
[tex]19-\frac{5}{2}x=34\ \ \ \ \ \ |subtract\ 19\ from\ both\ sides\\\\-\frac{5}{2}x=15\ \ \ \ \ |multiply\ both\ sides\ by\ (-\frac{2}{5})\\\\\boxed{x=-6} [/tex]