Can someone explain how to do this Optics question?

Question

A lamp and a screen are 1m apart and a +4.5D thin lens is mounted between them. Where must the lens be placed in order to produce a sharp image on the screen, what will be the magnification? There are two lens positions.

Answer 1

1)f = 1/D

2) 1/v + 1/u = 1/f

3) v + u = 1

4) D = 4.5

5) from 1) and 2); 1/v + 1/u = 4.5

6) rearrange 3); v = 1 - u

7) 6) into 5); 1/(1-u) + 1/u = 4.5

8) multiply 7) by u(1-u); u + 1-u = 4.5(1-u)u

9) expand and rearrange 8) 4.5u^2 - 4.5u + 1 = 0

10) by quadratic formula; u = {4.5 ±√(4.5² -4*4.5)}/9 = 1/2 ± 1/6

u = 1/3 m or 2/3 m