How to solve $ax+be^{cx}=d$

Question

Hi I have been trying to derive the formula for the range of a projectile with air resistance, and I've been trying to solve for time when $y=0$, and I have been left with an equation of the form $at+be^{ct}=d$, where $a$, $b$, $c$, $d$ are constants. I can't seem to find a solution anywhere, but it must since the projectile obviously has to hit the ground.

Answer 1

An answer involving the LambertW function is $$x = -{1\over c}\,{\rm LambertW} \left(b c e^{cd/a} \over a\right) + {d\over a}.$$ (Maple.)