There are natural numbers: $a$, $b$, $c$. 

$$\begin{cases}
ab+bc+ca+\frac32(a+b+c)=5015,\\
2abc-a-b-c=6366
\end{cases}
$$

I need to find the minimum value of $a+b+c$.
To my mind there's something connected with the derivative. I've already tried to find an equation for $a+b+c$, but I stuck right here.
If we do some math in the second equation, we can get this one

$a+b+c=3183/abc$
Everything's great, but if we consider $a+b+c = l$ (for example), then we need to find a minimum of this function. But as far as I'm concerned this is a Hyperbolic function, which doesn't have extreme values. So there's my first confusion.

Moving on I decided to do something with a first equation. But, unfortunately, no matter how I rearrange my $a$, $b$ and $c$ I get some equations and can't get anything useful out of it.

And the last thing. If I get an equation for $a+b+c$ from the first equation then find a derivative and its zero value, I get $c = -b$.

Well, that perfectly concludes the problem. Could anyone help me get this one done? 

Sorry for image confusion.