AHSME 1967 Problem 35

The roots of $64x^3-144x^2+92x-15=0$ are in arithmetic progression. The difference between the largest and smallest roots is: $\textbf{(A)}\ 2 \textbf{(B)}\ 1 \textbf{(C)}\ \frac{1}{2} \textbf{(D)}\ \frac{3}{8} \textbf{(E)}\ \frac{1}{4}$