# How to solve the equation $Axe^x - Bx - Ce^x + C = 0$ for $x$ where $A$,$B$ and $C$ are constants?

I have tried solving by using Taylor's series expansion for $e^x$ and approximating till the third term of the expansion (i.e. term with power 2). This gave me a quadratic equation which was easy to solve. But I am using the solution of this equation as part of a bigger numerical simulation using Finite Difference method. And the small error due to approximation in the expansion for $e^x$ accumulated over many iterations and gave erroneous results in the end.

So, I need some other way of solving this equation that does not involve approximation.

• you will Need a nmerical method, some sprecial cases can you solve symbolically – Dr. Sonnhard Graubner May 21 '17 at 7:18
• Dr. Sonnhard Graubner, could you elaborate on this ? I am using the Block Newton method. – P. Biswas May 21 '17 at 7:41
• Also, someone told me that the solution for this equation can be given Lambert function. Is this possible ? – P. Biswas May 21 '17 at 7:42
• no solution is found in Lamberd function here, try Wolfram alpha – Dr. Sonnhard Graubner May 21 '17 at 7:43
• see here for the Newton method keisan.casio.com/exec/system/1244946907 – Dr. Sonnhard Graubner May 21 '17 at 7:44