1. The problem is to solve the equation $x^2 - 5x + 6 = 0$. 2. We use the quadratic formula or factorization to solve quadratic equations. The quadratic formula is: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$, and $c$ are coefficients from the quadratic equation $ax^2 + bx + c = 0$. 3. For the equation $x^2 - 5x + 6 = 0$, the coefficients are $a=1$, $b=-5$, and $c=6$. 4. Let's try factorization first. We look for two numbers that multiply to $6$ and add to $-5$. These numbers are $-2$ and $-3$. 5. So, we can factor the equation as: $$ (x - 2)(x - 3) = 0 $$ 6. Setting each factor equal to zero gives the solutions: $$ x - 2 = 0 \Rightarrow x = 2 $$ $$ x - 3 = 0 \Rightarrow x = 3 $$ 7. Therefore, the solutions to the equation are $x = 2$ and $x = 3$. This means the quadratic equation $x^2 - 5x + 6 = 0$ has two roots: 2 and 3.