Consider the equation:
$2\sqrt {2x}+\sqrt {2x+3}=\sqrt {3x+2}+\sqrt {6x+20}.$
Find a trick ( if exists ) which allows to solve it elegantly i.e. with avoiding the systematic squaring.
(The systematic squaring inevitably leads to a fourth-degree equation:
$ \begin{align} 0 &= 207x^4-12564x^3+27738x^2+231084x-40401\\[6pt] &=9\left( 23x^2-1258x-4489\right) \left( x^2-6x+1\right)\;, \end{align} $ so the answer is $x=\dfrac {629+\sqrt {498888}} {23}.$