Your work so far is correct, rearranging the formula you have above will give you the following cubic equation:
Have you been taught how to solve cubic equations?
The problem states:The volume of the box is 630in^3. The height is 4 in more than the width, the length is 1 in more than than width.What is the width?
I started by forming the equation based on l*w*h=v so,
(1+w)(4+w)(w)=630 and i combined to get
w^3+5w^2+4w=630
And from this point I'm stuck