Where did the $x$ on the left side come from?
I would first just write:
$$t^3=\frac{6x^2+5}{2-5x^2}$$
Next, multiply through by $2-5x^2$ to get:
$$2t^3-5t^3x^2=6x^2+5$$
Now, what you want to do is arrange the equation with all the terms involving $x$ on one side and everything else on the other, the factor out $x^2$ and divide through by the other factor to solve for $x^2$ and then take the square root of both sides.
edit: I see you have also posted this at MMF and have been given the solution.