Volume is "width times height times length" and here, the width is 3- 2x, the height is x, and the length is 5- 2x. Thus, the volume is given by V= (3- 2x)(x)(5- 2x) which is a cubic equation, not a quadratic. IF you are given a specific volume, then you could solve that cubic equation for x.
It is also true that the area of a rectangle is "width times length" and the surface of this box consists of 5 rectangles, two with length= 5-2x and width x, two with length 3- 2x and height x, and one with length 5-2x and width 3-2x. The total surface area of the box is A= 2(5-2x)(x)+ 2(3-2x)(x)+ (5-2x)(3-2x) which, if you multiply it out is a quadratic equation. If you have a specific number for the surface area, then you could solve for x.
Now, what does the problem really ask you to do?