1. **Problem Statement:** Solve the equation $$x^2 - 5x + 6 = 0$$. 2. **Formula Used:** For quadratic equations of the form $$ax^2 + bx + c = 0$$, the solutions are given by the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 3. **Identify coefficients:** Here, $$a=1$$, $$b=-5$$, and $$c=6$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-5)^2 - 4 \times 1 \times 6 = 25 - 24 = 1$$ 5. **Find the roots:** $$x = \frac{-(-5) \pm \sqrt{1}}{2 \times 1} = \frac{5 \pm 1}{2}$$ 6. **Evaluate each root:** - $$x_1 = \frac{5 + 1}{2} = \frac{6}{2} = 3$$ - $$x_2 = \frac{5 - 1}{2} = \frac{4}{2} = 2$$ 7. **Answer:** The solutions to the equation are $$x=3$$ and $$x=2$$.