jmc

We see that we can rewrite the left side of the equation $8x^2-38x+35$ as $(2x-7)(4x-5)$, so we have $(2x-7)(4x-5)=0$. Thus, solving the equations $2x-7=0$ and $4x-5=0$ gives us $x=3.5$ and $x=1.25$ as our solutions. Since $1.25<3.5$, our final answer is $x=\boxed{1.25}$.