[tex]\pmb{x^{2} - 5x + 6 = 0} \\ \\ \Delta = b^{2}-4ac \\ \\ \Delta = (-5)^{2} - 4 \cdot 1 \cdot 6 = 25 - 24 = 1 \\ \\ \sqrt{\Delta} = 1 \\ \\ \boxed{x_{1} = \frac{-b- \sqrt{\Delta} }{2a} = \frac{5 - 1}{2 \cdot 1} = \frac{4}{2} = 2 }\\ \\ \boxed{x_{2} = \frac{-b + \sqrt{\Delta} }{2a} = \frac{5+1}{2\cdot 1 } = \frac{6}{2} = 3}[/tex]
--------------------------------------------------------
[tex]\pmb{x^{2} - 5x + 6 = 0} \\ \\ x^{2} - 3x - 2x + 6 = 0 \\ \\ x(x-3) - 2(x-3) = 0 \\ \\ (x-3)(x-2) = 0 \\ \\ x-3=0 \ \vee \ x-2 = 0 \\ \\ x=3 \ \vee \ x = 2 \\ \\ \boxed{x \in \lbrace 2, 3 \rbrace}[/tex]
