Make x the subject given the formula for y I am given the following formula:
$$y=\frac{x}{a}+\sqrt{\frac{x}{b}}.$$
I want to make x the subject.
I rearranged the equation and got to:
$$y^{4}=x(\frac{y^{2}}{2}+2y^{2})-x^{2}.$$
and I don't know where to go from here. May be this is the wrong rearrangement.
The answer according to wolfram alpha is:
$$x=\pm \frac{a^{\frac{3}{2}}\sqrt{a+4by}+a^{2}+2aby}{2b}.$$
How can I get there?

Hint: Set $u=y^2$ and solve the quadratic equation for $u$.
Then your equation is rewritten as
$$
u^2=\frac{5x}{2}u-x^2,
$$
which by completing the square is written as
$$
\Bigg(u-\frac{5}{4}x\Bigg)^2 - \frac{9}{16}x^2=0,
$$
and thus you have
$$
u-\frac{5}{4}x = \pm\frac{3}{4}x,
$$
or
$$
u = \pm\frac{3}{4}x+\frac{5}{4}x = \frac{5\pm3}{4}x.
$$
Finally $y=\sqrt{u}=\sqrt{\frac{5\pm3}{4}x}$.
