Answer
{$-8,-2,1,4$}
Work Step by Step
Since, $u^2+5u-14=0$
Factorize the expression as follows: $(u+7)(u-2)=0$
or, $u=${$-7,2$}
Replace $u$ with $(x-\dfrac{8}{x})$, we have
$(x-\dfrac{8}{x})=-7$
or, $x^2+7x-8=0$
or,$(x+8)(x-1)=0$
or, $x=${$-8,1$}
and $(x-\dfrac{8}{x})=2$
or, $x^2-2x-8=0$
or,$(x+2)(x-4)=0$
or, $x=${$-2,4$}
Hence, our solution set is $x=${$-8,-2,1,4$}
