the condition is that v is bigger or equal to 0

ive got ((0.2)v^2)/2 + 0.2g x 2.4 + 5((2.4 - L)^2)/2L = (5 x 1.6^2)/(2 x 0.8)

the answer given from here which i have no idea where it came from is:

L^2 -6.1184L + 5.76 smaller or equal to 0

implies 1.162 smaller or equal to L smaller or equal to 4.956

L bigger or equal to 1.162

I have no idea like i said where this working came from or how it works despite being in the mark scheme. If anyone coukd show me how this was derived you'd be saving my life i have an exam tomorrow and im sure this'll come up thnx