For which values of x is x^2 - 5x + 6 < 0 true?

Factorising the left hand side of the inequality gives (x-2)(x-3), so we know that the quadratic curve intersects the x-axis at x=2 and x=3. Since the coefficient of x^2 in the quadratic equation x^2-5x+6 is positive (+1), the graph of this equation is "u-shaped" (or "opens upwards") therefore on the y-axis, the curve is below 0 (y<0) between the points x=2 and x=3 on the x-axis.
Hence, the curve with the equation x^2-5x+6 is below the x-axis when 2<x<3, giving the answer as to when x^2-5x+6<0 is true.