+53 First find the value of \(x.\) Expanding and combining like terms, we find that it becomes a quadratic equation, \(5x^2+6x-18=0\).
Solving using the quadratic formula, we see that \(x\) has two solutions- \(\frac{-3\pm3\sqrt{11}}{5}\). We want the largest possible solution, so the \(\pm\) becomes a \(+\) instead.
Thus we have \(\frac{-3+3\sqrt{11}}{5}=\frac{a+b\sqrt{c}}{d}\). Substituting these values in for each other, we find that \(a=-3, b=3, c=11, d=5.\) So the value of \(\frac{acd}b=\frac{-3\cdot11\cdot5}{3}=\boxed{-55}.\)
