There are two solutions to the equation $3x^2+5x=-3x-4$.
The first solution is $x=-5/6-\sqrt{73}/6$. To find this solution, we can use the quadratic formula:
$$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
In this case, $a=3$, $b=5$, and $c=-4$. Substituting these values into the quadratic formula, we get:
$$x = \dfrac{-5 \pm \sqrt{5^2 - 4 \cdot 3 \cdot -4}}{2 \cdot 3}$$
$$x = \dfrac{-5 \pm \sqrt{73}}{6}$$
The second solution is $x=-5/6+\sqrt{73}/6$. This solution can be found by using the fact that the quadratic formula always gives two solutions, one negative and one positive.
Therefore, the two solutions to the equation $3x^2+5x=-3x-4$ are $x=-5/6-\sqrt{73}/6$ and $x=-5/6+\sqrt{73}/6$.