Question 582522
First, imagine doing this in real life. You have a sheet with length x and width x-15. When you cut out the corners, you change the dimensions, but you don't change the difference between them, so you're still looking at something like length y and width y-15, and now you have a third dimension (height) from folding those three-inch-wide flaps upward. This gives you a volume of

{{{3y(y-15)=1938}}}

This can be reworked into the quadratic equation

{{{y^2-15y-646=0}}}

The quadratic formula then gives the solution y = 34, the length of your box. Then y - 15 = 19 provides the width, and of course the height is 3 inches.

How do you find the original dimensions? Remember that each edge of your sheet lost 3 inches on both sides, for a total of 6 inches lost, so y = x - 6. All you need to do in order to find the original dimensions is add those 6 inches back:

{{{x=y+6=40}}}

{{{x-15=y+6-15=25}}}

There you have the original length and width of your sheet. I hope this explanation has been clear and helpful.