A screen is placed 90cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20cm .Determine the focal length of the lens.(ncert, pg no:347, Q.no:9.20...)

Can you please explai without using the displacement formula...because displacement formula is not there in our portion and i didn't understand where it came from?

Dear Student ,
I don't know why the displacement formula is not there in this portion .But believe  it or not displacement formula is the best and easier method to solve this type of problems .You can derive the displacement formula from the lens makers formula .
Here I am again trying to clear your doubt .
Distance between the image (screen) and the object is = D =90 cm 
Distance between the two locations of convex lens = d= 20 cm 
Let the focal length of the lens is f .
Focal length is related to d and D as :
$$\begin{gathered} f=\frac{D^2-d^2}{4D} \\ =\frac{{\left(90\right)}^2-{\left(20\right)}^2}{4\times 90} \\ =\frac{7700}{360} \\ =21·39 cm \\ Therefore focal length of the convex lens is 21·39 cm . \end{gathered}$$
Hope it helps you and in my personal opinion I want to say that use this formula to solve this types of problems in future .
Regards