X²−5x+6=0 solve

The quadratic equation is in the form $ax^2 + bx + c = 0$, where $a=1$, $b=-5$, and $c=6$.

We need to find two numbers that multiply to $c$ (which is 6) and add up to $b$ (which is -5).
The numbers are -2 and -3, because $(-2) \times (-3) = 6$ and $(-2) + (-3) = -5$.

Rewrite the equation using these numbers:
$(x - 2)(x - 3) = 0$

For the product of two factors to be zero, at least one of the factors must be zero.
$x - 2 = 0 \quad \text{or} \quad x - 3 = 0$

$x = 2 \quad \text{or} \quad x = 3$