Question

como resolver (x-1)(x-2)=6

Answer 1

Distributiva

(x-1)(x-2)=6
x² - 2x - x + 2 = 6
x² - 3x + 2 - 6 = 0 
x² - 3x - 4 = 0

a = 1
b = -3
c = -4

Δ = b² -4 .a . c
Δ = (-3)² -4 . 1 . (-4)
Δ = 9 - 4 . (-4)
Δ = 9 + 16
Δ = 25

$\mathtt{\dfrac{-b+-~\sqrt{\Delta}}{2~~.~a}~~=~~\dfrac{-(-3) +-~\sqrt{25}}{2~~.~~1}~~=~~\dfrac{3+-~5}{2}} \\ \\ \\ \mathtt{x' = \dfrac{3 + 5}{2}~~=~~\dfrac{8}{2}~~=~~4} \\ \\ \\ \mathtt{x'' = \dfrac{3 - 5}{2}~~=~~-\dfrac{2}{2}~~=~~-1}$

Resposta: S{-1 , 4}