1. **State the problem:** Solve the quadratic equation $$x^2 - 3x + 2 = 0$$. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = -3$$, and $$c = 2$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-3)^2 - 4 \times 1 \times 2 = 9 - 8 = 1$$. 5. **Find the roots:** $$x = \frac{-(-3) \pm \sqrt{1}}{2 \times 1} = \frac{3 \pm 1}{2}$$. 6. **Evaluate each root:** - $$x_1 = \frac{3 + 1}{2} = \frac{4}{2} = 2$$ - $$x_2 = \frac{3 - 1}{2} = \frac{2}{2} = 1$$ 7. **Conclusion:** The solutions to the equation $$x^2 - 3x + 2 = 0$$ are $$x = 1$$ and $$x = 2$$.