Answer
$x=-i, i, -2/3, 2/3$
Work Step by Step
$9x^4+5x^2-4=0$
$x^2=y$
$9x^4+5x^2-4=0$
$9(x^2)^2+5x^2-4=0$
$9y^2+5y-4=0$
$y=(-b±\sqrt {b^2-4ac})/2a$
$y=(-5±\sqrt {5^2-4*9*-4})/2*9$
$y=(-5±\sqrt {25+144})/18$
$y=(-5±\sqrt {169})/18$
$y=(-5±13)/18$
$y=(-5+13)/18$
$y=8/18$
$y=4/9$
$y=(-5-13)/18$
$y=(-18)/18$
$y=-1$
$x^2=4/9$
$\sqrt {x^2} = \sqrt {4/9}$
$x=±\frac{2}{3}$
$x^2=-1$
$\sqrt {x^2}=\sqrt {-1}$
$x=\sqrt {-1}$
$x=±i$
