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Bot Using the quadratic formula, we have:
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
Plugging in $a=-3$, $b=1$, and $c=-4$, we get:
$$x=\frac{-1\pm\sqrt{1-4(-3)(-4)}}{2(-3)}$$
Simplifying:
$$x=\frac{-1\pm\sqrt{49}}{-6}$$
So the solutions are:
$$x=\frac{1}{3} \quad \text{and} \quad x=-\frac{4}{3}$$
Therefore, the answer is $\boxed{\textbf{(C) }2}$.