ПОМОГИТЕ ПЛИЗ lg(2x-1)+lg(x-9)=2

Решите задачу:

$lg(2x-1)+lg(x-9)=2\; ,\; \; ODZ:\; \left \{ {{2x-1\ \textgreater \ 0} \atop {x-9\ \textgreater \ 0}} \right. \; \left \{ {{x\ \textgreater \ \frac{1}{2}} \atop {x\ \textgreater \ 9}} \right. \; ,x\ \textgreater \ 9\\\\lg(2x-1)(x-9)=lg10^2\\\\2x^2-19x+9=100\\\\2x^2-19x-91=0\\\\D=361+728=1089,\; \; \sqrt{D}=33\\\\x_1=\frac{19-33}{4}=-\frac{14}{4}=-\frac{7}{2}=-3,5\notin ODZ\\\\x_2=\frac{19+33}{4}=13\\\\Otvet:\; \; x=13.$