Given a radical equation of the form $$0=\sum_{j=1}^n a_j\sqrt{|b_j-x|}$$ where $b_j>0$ and the sign of $a_j\in\mathbb R$ matches that of $b_j-x$, is there any more efficient (analytical?) solution for $x$ than iteratively putting one square root to the other side, squaring twice (to get rid of the absolute value), isolating another root and repeating, effectively yielding a polynomial of an order that increases with $n$? Is there some upper limit on $n$ for which an analytical solution exists?
edit The simplification I meant to do was allowing $a_j^2\in\mathbb R$ (i.e. $a_j$ may be purely imaginary as well) such that $a_j^2(b_j-x)\ge0$, reducing the original equation to $$0=\sum_{j=1}^n a_j\sqrt{b_j-x}$$ so squaring is required only once.