problem solving - square roots

This problem was in my calculus exercise, yet I don't understand why:

Solve the equation :

(Show there are not other solutions to the ones you found)

Now, solving it regularly using simple algebra got me into an eighth-degree polynomial, which reminded my my teachers have just told us there are proofs for why there are no 'formulas' for solving polynomial equations higher than 5.

Anyway, how can I solve this problem using calculus tools? I thought of doing the following thing:

We know that , therefore:

.

Let the first expression be , ane the second expression be . Therefore:

Therefore,

but how do I find it :) ?