Question

(x-1)(x-2)=6 resolva essa equação por favor :)

Answer 1

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

*Encontrando o delta:

∆=b²-4ac

∆=9-4×1×(-4)
∆=9 + 16
∆=25

*Encontrando as raízes (valor de x), pela fórmula de Bhaskara:

x= (-b ± √∆)/2a
x=(-3±√25)/2×1
x=(-3±5)/2

x'=(-3+5)/2
x'= 2/2
x'=1

x''=(-3-5)/2
x"=-8/2
x"=-4

Answer 2

$(x-1)(x-2)=6 \\ x^2-2x - x + 2=6 \\ x^2-3x+2-6=0 \\ x^2-3x-4=0 \\ \\ a = 1 \\ b=-3 \\ c=-4 \\ \\ x= \dfrac{-b\pm \sqrt{b^2-4\,a\,c} }{2\,a} \\ \\ \\ x= \dfrac{-(-3)\pm \sqrt{(-3)^2-4\cdot1\cdot(-4)} }{2\cdot1} \\ \\ \\ x= \dfrac{3\pm \sqrt{9-(-16)} }{2} \\ \\ \\ x = \dfrac{3\pm \sqrt{25} }{2} \\ \\ \\ x= \dfrac{3\pm5}{2} \\ \\ \\ x' = \frac{3+5}{2} \rightarrow\boxed{x'=4} \\ \\ x''= \frac{3-5}{2} \rightarrow \boxed{x''=-1}$