I'm not getting this one.

$\displaystyle 3z^4 - 5z^2 +1 = 0$

If I substitute variable u in place of $\displaystyle z^2$, I get

$\displaystyle 3u^2 - 5u + 1 = 0$

solving with the Quadratic Equation gives me

$\displaystyle u= 5 \pm \frac{\sqrt13}{6}$

and since u = $\displaystyle z^2$, the solutions should be

z = $\displaystyle \pm \sqrt{5 \pm \frac{\sqrt13}{6}}$

But, the book says the solution is

$\displaystyle z = \pm \frac{ \sqrt{30 \pm 6\sqrt13}} {6}$

What have I done wrong?