Find the roots of x² − 5x + 6 = 0 using the quadratic formula. Show all steps and write the final answer with the math in LaTeX.

For a quadratic equation in the form $ax^2 + bx + c = 0$, we have:
$a = 1$
$b = -5$
$c = 6$

The quadratic formula is given by:
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(6)}}{2(1)}$

$x = \frac{5 \pm \sqrt{25 - 24}}{2}$
$x = \frac{5 \pm \sqrt{1}}{2}$
$x = \frac{5 \pm 1}{2}$

For the positive sign:
$x_1 = \frac{5 + 1}{2} = \frac{6}{2} = 3$

For the negative sign:
$x_2 = \frac{5 - 1}{2} = \frac{4}{2} = 2$

The roots of the equation $x^2 - 5x + 6 = 0$ are $x=2$ and $x=3$.