How Are g1, g2, g3 Derived and What Does L Represent in Numerical Analysis?

[nhrock3]

http://i48.tinypic.com/2yzd213.jpg

how they got g1 g2 g3
?

 

[HallsofIvy]

To get g_1, they simply added x to both sides of x^3- x- 5= 0 to get x^3- 5= x.

To get g_2, they added x+ 5 to both sides to get x^3= x+ 5 and took the cube root of both sides.

To get g_3, they subtracted 5 from both sides to get x^3- x= 5, then factored, x(x^2- 1)= 5 and, finally, divided both sides by x^2- 1 to get x= 5/(x^2- 1).

 

[nhrock3]

ok i solved a similar equation:
x^3+2x^2+4-x=0
g1=x^3+2x^2+4

why for g1 L=0.5
how to find L for other g
what is the meaning of L?