Question

What is the answer to
-5/6+x/6=1/x

Answer 1

`-(5)/(6)+(x)/(6)=(1)/(x)|\cdot6x\qquad(x \\ot=0)\\ -5x+x^2=6\\ x^2-5x-6=0\\ x^2+x-6x-6=0\\ x(x+1)-6(x+1)=0\\ (x-6)(x+1)=0\\ x=6 \vee x=-1`

Answer 2

`-5/6+x/6=1/x\Leftrightarrow x^2-5x-6=0`


`\Delta=25+24=7^2` hence the answer is
`(5\pm7)/(2)=\left\lbrace-1,6\right\rbrace`