Answer :
The given equation is:
[tex](3m-4)x^2-(2m+1)x-3m-1=0[/tex]The equation will have distinct roots if:
[tex]\begin{gathered} (2m+1)^2-4(3m-4)(-3m-1)\ge0_{} \\ 4m^2+4m+1-4(-9m^2+12m-3m+4)\ge0 \\ 4m^2+4m+1+36m^2-36m-16\ge0 \\ 40m^2-32m-15\ge0 \end{gathered}[/tex]Solve for zero to get:
[tex]m=\frac{8+\sqrt[]{214}}{20},\frac{8-\sqrt[]{214}}{20}[/tex]