1. Let's consider the problem: Solve the quadratic equation $$x^2 - 5x + 6 = 0$$ on your own. 2. The formula to solve quadratic equations is the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$, and $c$ are coefficients from the quadratic equation $ax^2 + bx + c = 0$. 3. Important rules: - Calculate the discriminant $\Delta = b^2 - 4ac$. - If $\Delta > 0$, there are two real and distinct solutions. - If $\Delta = 0$, there is one real solution. - If $\Delta < 0$, there are no real solutions (complex solutions). 4. For the equation $x^2 - 5x + 6 = 0$, identify $a=1$, $b=-5$, and $c=6$. 5. Calculate the discriminant: $$\Delta = (-5)^2 - 4 \times 1 \times 6 = 25 - 24 = 1$$ 6. Since $\Delta = 1 > 0$, there are two real solutions. 7. Apply the quadratic formula: $$x = \frac{-(-5) \pm \sqrt{1}}{2 \times 1} = \frac{5 \pm 1}{2}$$ 8. Calculate the two solutions: $$x_1 = \frac{5 + 1}{2} = 3$$ $$x_2 = \frac{5 - 1}{2} = 2$$ 9. Final answer: The solutions to the equation are $x=3$ and $x=2$. Try solving this on your own to practice!