I'm trying to prove that u=A+square root(A^2 -1 ), and d=1/u, when

A=1/2((e^-rδt ) +e^(r+σ^2 )δt)

So I set σ^2 δt+e^2rδt -d^2 / (~~(u-d)~~(u+d) =(e^rδt -d)/~~(u-d)~~)

and we know that u=(1/d) so plug that in that equation.

σ^2 δt+e^2rδt -d^2 / ((1/d)+d) =e^rδt-d,

((1/d)+d) * (e^rδt -d) = (1/d)*e^rδt -1 + de^rδt -d^2

σ^2 δt+e^2rδt -d^2 = (1/d)*e^rδt -1 + de^rδt -d^2

bring everything to one side and set it equal to 0.

So I guess, Solve for d first.