Question: I have the following python code:

```
ymin = 1615.72687
ymax = -1607.73011
ec50 = 2.19835099
x,y = symbols('x y')

expression = ((y-ymin)*(ec50+x))+abs(ymax)*x
equation = solve(expression,x)

```

And it spits out the following equation: `[0.5495877475*(-100000.0*y + 161572687.0)/(25000.0*y - 199919.0)]`

`solve` sets `expression` equal to $0$ and solves for `x`. When I tried to do this by hand, I received the following answer: $$x = \frac{(y)(ec50) - (ymin)(ec50)}{\mid{ymax}\mid - y -ymin}$$

Hence, I don't see how that equation translates to what was outputted by Python. Also, my assumption for Python multiplying `y` by $100000.0$ is to compensate for the shift in the other variables. But even taking that into consideration doesn't help me understand the discrepancy between the two equations.

Answer: 
$\newcommand{\bbx}[1]{\,\bbox[8px,border:1px groove navy]{\displaystyle{#1}}\,}
 \newcommand{\braces}[1]{\left\lbrace\,{#1}\,\right\rbrace}
 \newcommand{\bracks}[1]{\left\lbrack\,{#1}\,\right\rbrack}
 \newcommand{\dd}{\mathrm{d}}
 \newcommand{\ds}[1]{\displaystyle{#1}}
 \newcommand{\expo}[1]{\,\mathrm{e}^{#1}\,}
 \newcommand{\ic}{\mathrm{i}}
 \newcommand{\mc}[1]{\mathcal{#1}}
 \newcommand{\mrm}[1]{\mathrm{#1}}
 \newcommand{\pars}[1]{\left(\,{#1}\,\right)}
 \newcommand{\partiald}[3][]{\frac{\partial^{#1} #2}{\partial #3^{#1}}}
 \newcommand{\root}[2][]{\,\sqrt[#1]{\,{#2}\,}\,}
 \newcommand{\totald}[3][]{\frac{\mathrm{d}^{#1} #2}{\mathrm{d} #3^{#1}}}
 \newcommand{\verts}[1]{\left\vert\,{#1}\,\right\vert}$
\begin{align}
{1 \over 2\ic}\sum\_{n \not= 0}{\expo{\ic nx} \over n} & =
{1 \over 2\ic}\sum\_{n = 1}^{\infty}
\pars{{\expo{\ic nx} \over n} + {\expo{-\ic nx} \over -n}} =
\sum\_{n = 1}^{\infty}{\sin\pars{nx} \over n} =
x\sum\_{n = 1}^{\infty}\mrm{sinc}\pars{nx}
\\[5mm] & =
-x + x\sum\_{n = 0}^{\infty}\mrm{sinc}\pars{nx} =
-x + x\bracks{\mrm{sgn}\pars{x}\,{\pi \over 2} + {1 \over 2}} =
\bbx{\ds{\pi\verts{x} - x \over 2}}
\end{align}
There are many ways to "sum over all nonzero integers". When the convergence is not absolute (as in this case) I think $$\displaystyle\sum\_{n\neq0}$$ is ambiguous if not previously defined.

In this case it most likely means that it is the limit of partial *symmetric* sums$$\displaystyle\sum\_{n\neq0}=\displaystyle\lim\_{k\to\infty}\sum\_{\substack{-k\leq n\leq k \\ n\neq0}}$$
With this definition your series converges at $x=0$ with value $0$.