X^(4/3) - 6X^(2/3) = -8
and
9^(2x) - 2*9^x = 3
Thanks!!
These are simple quadratic forms. You must see the relationship to all other quadratics you have encountered.
$\displaystyle a\cdot Something^{2}\;+\;b\cdot Something\;+\;c\;=\;0$
Then, $\displaystyle Something\;=\;\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$
This should be familiar.
That would depend on your substitution. What did you do? Normally, you would want to change variables. Using 'x' both before and after is certainly bad form, but mostly it's just confusing.
Try $\displaystyle y = x^{2/3}$ and write the whole thing in terms of 'y'.