Question

a equaçao resolvida
e) x(X-2)=2(x+6)

Answer 1

$x(x-2)=2(x+6)\to \\\\ x^{2} -2x=2x+12\to \\\\x^{2} -2x-2x-12=0\to\\\\ x^{2} -4x-12=0\\\\ a=1\ ;\ b=-4\ ;\ c=-12\\\\\\ \Delta=b^2-4ac\to \Delta=(-4)^2-4*1*(-12)\to \Delta=16+48\to \Delta=64\\\\ x' \neq x''\\\\ \\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-(-4)\pm \sqrt{64} }{2*1} \to x= \frac{4\pm 8}{2} \to \\\\\\ x'= \frac{4+ 8}{2} \to x'= \frac{12}{2} \to x'=6\\\\\\ x''= \frac{4- 8}{2} \to x''= \frac{-4}{2} \to x''=-2\\\\\\\\ S=\{-2;6\}$