smc

Note that this equation is of the form $a^2+ab=0$, which factors to $a(a+b)=0$. Plugging in $a=x-\frac{3}{4}$ and $b=x-\frac{1}{2}$ gives: $(x-\frac{3}{4})(x-\frac{3}{4}+x-\frac{1}{2})=0$ $(x-\frac{3}{4})(2x-\frac{5}{4})=0$ The roots are $x=\frac{3}{4}$ nad $x=\frac{1}{2}\cdot \frac{5}{4}$. The smaller root is $\frac{5}{8}$, which is option $\boxed{\frac{5}{8}}$.