Four points $A(6,3),B(-3,5),C(4,-2)$ and $D(x,3x)$ are given in such a way that $\large\frac{\Delta DBC}{\Delta ABC}=\frac{1}{2}$, then the value of x is _______

Question

$\begin{array}{1 1}(A) \;\large\frac{-11}{8},\frac{-3}{8} \\(B)\; \large\frac{11}{8},\frac{3}{8} \\(C)\;\large\frac{-11}{8}, \frac{3}{8} \\(D)\;\large\frac{11}{8},\frac{-3}{8} \end{array}$