1. **Problem:** Solve the equation $$x^2 - 4x + 3 = 0$$ 2. **Formula:** Use the quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $$a=1$$, $$b=-4$$, and $$c=3$$. 3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-4)^2 - 4 \times 1 \times 3 = 16 - 12 = 4$$ 4. **Apply the quadratic formula:** $$x = \frac{-(-4) \pm \sqrt{4}}{2 \times 1} = \frac{4 \pm 2}{2}$$ 5. **Find the two solutions:** - $$x_1 = \frac{4 + 2}{2} = \frac{6}{2} = 3$$ - $$x_2 = \frac{4 - 2}{2} = \frac{2}{2} = 1$$ 6. **Answer:** The solutions are $$x = 3$$ and $$x = 1$$.