Answer
No real solutions
Work Step by Step
Using the quadratic equation to solve the equation, we find:
$$x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:4\cdot \:9}}{2\cdot \:4} $$
The value under the radical is negative, so there are no real solutions. The imaginary solutions are:
$$x=\frac{3}{4}+i\frac{3\sqrt{3}}{4},\:x=\frac{3}{4}-i\frac{3\sqrt{3}}{4}$$
