I have the following equation:
$$ \left(\frac{\sqrt{d_B}-\sqrt{d_{Beq}}}{\sqrt{d_{Bmin}}-\sqrt{d_{Beq}}} \right)^{1-\frac{c1}{c2}}\left(\frac{\sqrt{d_B}+\sqrt{c3}}{\sqrt{d_{Bmin}}+\sqrt{c3}} \right)^{1+\frac{c1}{c2}}=exp\left(-0.3 \frac{z-z_0}{d_D}\right) $$
The equation is basically in the form of $(a)^x(b)^y=exp(c)$. All of the terms, $d_{Beq}, d_{Bmin}, c1, c2, c3, z, z_0, d_D$ are solved from other equations, so they are known.
Is it possible to solve the equation for $d_B$?
Not in the general case. Assuming ${c1\over c2}$ to be a fraction smaller than one, by raising both members to the power $c2$ you would obtain a polynomial in $\sqrt{d_B}$, not solvable by radicals (except degree < 5).