1. The problem asks us to find the sum of the roots of the quadratic equation $$3x^2 + 14x - 5 = 0$$. 2. Recall that for a quadratic equation $$ax^2 + bx + c = 0$$, the sum of the roots $$\alpha + \beta$$ is given by $$-\frac{b}{a}$$. 3. Here, $$a = 3$$ and $$b = 14$$, so the sum of the roots is: $$\alpha + \beta = -\frac{14}{3}$$. 4. Therefore, the sum of the roots is $$-\frac{14}{3}$$.