1. **State the problem:** Solve the quadratic equation $$x^2 + 9x + 2 = 0$$. 2. **Formula used:** The quadratic formula for solving $$ax^2 + bx + c = 0$$ is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = 9$$, and $$c = 2$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 9^2 - 4 \times 1 \times 2 = 81 - 8 = 73$$. 5. **Evaluate the roots:** Since $$\Delta > 0$$, there are two distinct real roots: $$x = \frac{-9 \pm \sqrt{73}}{2}$$. 6. **Final answer:** $$x_1 = \frac{-9 + \sqrt{73}}{2}, \quad x_2 = \frac{-9 - \sqrt{73}}{2}$$. These are the solutions to the quadratic equation.