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. We try to factor the quadratic: $$x^2 - 5x + 6 = (x - 2)(x - 3) = 0$$ 5. Setting each factor equal to zero gives the solutions: $$x - 2 = 0 \Rightarrow x = 2$$ $$x - 3 = 0 \Rightarrow x = 3$$ 6. Therefore, the solutions to the equation are $x = 2$ and $x = 3$.