I've empiricaly produced this exponential equation to express a graphical representation :
$$ y = \left(a^x + (bx)²\right) \left((1-10^{-x}) x\right) $$
I know the constants $a$ and $b$.
Now, i would like to extract the formula to be able to calculate x plots separatively.
How can i factor this equation to solve x ?
$$ x = ?$$
I didnt practice maths for so many years, i almost completely forgot all of the factorisation rules so im likely stucked...
Some help would be greatly appreciated.
EDIT :
I forgot to say that A and B values can be restricted to a range allowing to find an acceptable solution. For example, a = 1 and b = 10
You can view the representation result in this spreadsheet : https://docs.google.com/spreadsheet/ccc?key=0AiLgphtsXoERdDN2Y2RTeUlEa1FaNFdSM3dsT0I5V3c
That is too complicated to solve explicitly, but it may be possible to solve numerically, if there is a solution (assuming $a$ is positive, there may be some negative values of $y$ for which there is no real solution).
For example if $y=2$, $a=3$ and $b=4$ then $x \approx -0.403132$ and $x \approx 0.503299$ are solutions.