1. **State the problem:** Given the quadratic equation $$2y^2 - 5y - 3 = 0$$ with roots $$\alpha$$ and $$\beta$$, find the value of $$\alpha + \beta$$. 2. **Recall the formula:** For a quadratic equation $$ay^2 + by + c = 0$$, the sum of the roots is given by $$\alpha + \beta = -\frac{b}{a}$$. 3. **Identify coefficients:** Here, $$a = 2$$, $$b = -5$$, and $$c = -3$$. 4. **Calculate the sum of roots:** $$\alpha + \beta = -\frac{-5}{2} = \frac{5}{2}$$. 5. **Conclusion:** The sum of the roots $$\alpha + \beta$$ is $$\frac{5}{2}$$.