Take the 2-minute tour ×  I build a model for our problem, but i
cannot get a result from my model. Could anyone give me some
idea to solve this formula: $aX+bX^2=e^{cX}$  Thx in advance!
share|improve this question What is $a$, $b$ and $c$? I assume
those are constants and you want to solve for $X$? It seems
unlikely that you can get closed formulas for $X$. other than in
very special cases. For fixed $a$, $b$ and $c$ any standard
numerical method for solving equations should suffice. (Newton's
method, bisection, or some variant of those.) –  mrf May 22 '12
at 9:54 Newton's method will converge for "most" values of
$a,b,c$ but studying precisely each case could be time-
consuming. You may start with $(a,b,c)=(1,1,1)$, the function is
convex near its negative $0$, and use a homotopy method to reach
all other values of $(a,b,c)$. Matlab or Mathematica will solve
this for you efficiently too. I do not think there is an
explicit solution in terms of roots exponentials and logarithms
but I would be greatly intere