Answer
$x=-1/8, 27$
Work Step by Step
$2x^{2/3}-5x^{1/3}=3$
$2x^{2/3}-5x^{1/3}-3=3-3$
$2x^{2/3}-5x^{1/3}-3=0$
$x^{1/3}=y$
$2x^{2/3}-5x^{1/3}-3=0$
$2(x^{1/3})^2-5x^{1/3}-3=0$
$2y^2-5y-3=0$
$(2y+1)(y-3)=0$
$2y+1=0$
$2y=-1$
$2y/2=-1/2$
$y=-1/2$
$y-3=0$
$y=3$
$x^{1/3}=y$
$x^{1/3}=-1/2$
$(x^{1/3})^3=(-1/2)^3$
$x=-1/8$
$x^{1/3}=y$
$x^{1/3}=3$
$(x^{1/3})^3=3^3$
$x=27$