If $x\Big\lfloor x \big\lfloor x\lfloor x \rfloor \big\rfloor \Big\rfloor=2018$, find $x$.

My working: if $x$ is positive then by estimation it must be in $(6,7)$ and for this interval I : $x\Big\lfloor x \big\lfloor x\lfloor x \rfloor \big\rfloor \Big\rfloor<2003$. So no solution for positive $x$.

For negative $x$, I got $x \in (-7,-6)$ and using this I got $x=\frac{2018}{k}, k$ can be $-336,-335,\cdots,-289,$
Now using excel sheet I got $x=-\frac{2018}{305}$.