Answer
$y=1/3, -1/3, i\sqrt 6/3, -i\sqrt 6/3$
Work Step by Step
$27y^4+15y^2=2$
Let $x=y^2$
$27y^4+15y^2=2$
$27(y^2*y^2)+15(y^2)=2$
$27x^2+15x=2$
$27x^2+15x-2=2-2$
$27x^2+15x-2=0$
Let $a=27$, $b=15$, $c=-2$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-15±\sqrt {15^2-4*27*-2})/2*27$
$x=(-15±\sqrt {225+216})/54$
$x=(-15±\sqrt {441})/54$
$x=(-15±21)/54$
$x=(-15-21)/54$
$x=-36/54$
$x=-2/3$
$x=(-15±21)/54$
$x=(-15+21)/54$
$x=6/54$
$x=1/9$
$x=-2/3, 1/9$
$x=y^2$
$y^2=1/9$
$\sqrt {y^2} = \sqrt {1/9}$
$y = \sqrt 1/ \sqrt 9$
$y = ±1/±3$
$y=1/3, 1/-3, -1/3, -1/-3$
$y=1/3, -1/3$
$y^2=-2/3$
$\sqrt {y^2} = \sqrt {-2/3}$
$y = \sqrt -2/ \sqrt 3$
$y = \sqrt -2*\sqrt 3/ \sqrt 3*\sqrt 3$
$y=\sqrt -6 / 3$
$y=\sqrt {-1*6} /3$
$y=i\sqrt 6/3$
$y=i\sqrt 6/3, -i\sqrt 6/3, i\sqrt 6/-3, -i\sqrt 6/-3$
$y=i\sqrt 6/3, -i\sqrt 6/3$
$y=1/3, -1/3, i\sqrt 6/3, -i\sqrt 6/3
