1. **State the problem:** Given the quadratic equation $$20x^2 - 23x + 6 = 0$$ with roots $$x_1$$ and $$x_2$$, find the value of $$x_1 \times x_2 + x_1 + x_2$$. 2. **Recall the formulas:** For a quadratic equation $$ax^2 + bx + c = 0$$, the sum and product of roots are: $$x_1 + x_2 = -\frac{b}{a}$$ $$x_1 \times x_2 = \frac{c}{a}$$ 3. **Identify coefficients:** Here, $$a = 20$$, $$b = -23$$, and $$c = 6$$. 4. **Calculate sum of roots:** $$x_1 + x_2 = -\frac{-23}{20} = \frac{23}{20}$$ 5. **Calculate product of roots:** $$x_1 \times x_2 = \frac{6}{20} = \frac{3}{10}$$ 6. **Find the required expression:** $$x_1 \times x_2 + x_1 + x_2 = \frac{3}{10} + \frac{23}{20} = \frac{6}{20} + \frac{23}{20} = \frac{29}{20}$$ 7. **Final answer:** $$\boxed{\frac{29}{20}}$$