Question

como resolvo essa equação de 2° grau? (x-1) (x-2) = 6

Answer 1

$(x - 1)\cdot(x-2)=6\\\\(x-1)\cdot(x-2)-6=0\\\\x^2-2x-x+2-6=0\\\\x^2-3x-4=0\\\\\boxed{a=1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,b=-3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,c=-4}\\\\\triangle=b^2-4ac\\\triangle=(-3)^2-4.(1).(-4)\\\triangle=9+16\\\triangle=25\\\\x= \dfrac{-b \frac{+}{-} \sqrt{\triangle} }{2a} \\\\\\x= \dfrac{-(-3) \frac{+}{-} \sqrt{25} }{2}\\\\\\x= \dfrac{3 \frac{+}{-}5 }{2}\\\\\\x'= \dfrac{(3+5)}{2}\\\\\\x'=4\\\\\\x"= \dfrac{3-5}{2}\\\\\\x"=-1\\\\\\ \boxed{S={(-1,4)}}$