How do I find/estimate the unknown given that the equation has exactly $2$ solutions? My problem: 

The equation $x(x^2-7) = 2x+c$ has exactly $2$ solutions. Estimate the value(s) of $c$, writing you answer(s) in the form $c_1< c <c_2$, where $c_1$ and $c_2$ are integers.

My question: How do "$2$ solutions" contribute to finding $c$? Like I couldn't find any relation between them. 
Thank you.

Consider $f(x)=x^3-9x$.
Now, $$f'(x)=3x^2-9=3(x-\sqrt3)(x+\sqrt3).$$
For $f'(x)=0$ we obtain $x=\sqrt3$ or $x=-\sqrt3$.
For $x=\sqrt3$ we obtain $c=-6\sqrt3$ and 
$$x(x^2-7)-2x-c=0$$ it's
$$(x-\sqrt3)^2(x+2\sqrt3)=0,$$ which has two different roots.
For $x=-\sqrt3$ we obtain $c=6\sqrt3$ and the following equation.
$$(x+\sqrt3)^2(x-2\sqrt3)=0.$$
