Solve the equation $x^2+6x=-\frac{11}{4}$.

A$x=-3$ and $x=2$

B$x=-2$ and $x=3$

C$x=\frac{1}{2}$ and $x=-\frac{11}{2}$

D$x=-\frac{1}{2}$ and $x=-\frac{11}{2}$