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. Here, factorization is simpler. 3. Factor the quadratic expression: $$x^2 - 5x + 6 = (x - 2)(x - 3)$$ 4. Set each factor equal to zero: $$x - 2 = 0 \quad \text{or} \quad x - 3 = 0$$ 5. Solve each equation: $$x = 2 \quad \text{or} \quad x = 3$$ 6. Therefore, the solutions to the equation are $x = 2$ and $x = 3$. This means the parabola crosses the x-axis at these points.