Answer
$y=-i\frac{\sqrt 6}{3}, i\frac{\sqrt 6}{3}, \frac{-1}{3}, \frac{1}{3}$
Work Step by Step
$27y^4+15y^2=2$
$y^2=x$
$27y^4+15y^2=2$
$27(y^2)^2+15y^2=2$
$27x^2+15x-2=0$
$(9x-1)(3x+2)=0$
$9x-1=0$
$9x=1$
$9x/9=1/9$
$x=1/9$
$3x+2=0$
$3x=-2$
$3x/3=-2/3$
$x=-2/3$
$y^2=x$
$y^2=1/9$
$\sqrt{y^2}=\sqrt{1/9}$
$y=±\frac{1}{3}$
$y^2=x$
$y^2=\frac{-2}{3}$
$\sqrt{y^2}=\sqrt{\frac{-2}{3}}$
$y=\sqrt {\frac{-1*2}{3}}$
$y=\sqrt {\frac{-1*2}{3}}(\sqrt {\frac {3}{3}})$
$y=\sqrt {\frac{-1*2*3}{3*3}}$
$y=\frac {\sqrt {-1*2*3}}{\sqrt {3*3}}$
$y=\frac {\sqrt {-1*6}}{3}$
$y=±i\frac {\sqrt {6}}{3}$
