Question 983709
u, edge of each identical cut-out square
w, width of rectangular cardboard
L, length of cardboard
v, volume of the open-top box


The box is u tall and the base is  (w-2u)(L-2u).
The volume is  {{{highlight_green((w-2u)(L-2u)*u=v)}}}.


Solve for u.


{{{(wL-2uL-2uw+4u^2)u=v}}}
{{{4u^3-2Lu^2-2wu^2+wLu-v=0}}}
{{{highlight_green(4u^3-(2L+2w)u^2+wLu-v=0)}}}-----Now we need to plug-in the known values for the cubic equation.


{{{4u^3-39u^2+92u-63.75=0}}}
Integers are preferred so multiply by 4...
{{{cross(16u^4-156u^2+368u-255=0)}}}---possibly wrong - did not work-


The roots (if Rational Roots Theorem)  we want must be positive but certainly much less than 8.  Most sensible to first check for 1 and 3  (both are factors of 255).


I used a graphing tool. 
...   graph shows roots at u=1.5 and u=1.6.