+129852 x^2 + (a - (1/a))x - 1 = 0
x^2 +[ (a^2 - 1) / a ]x - 1 = 0 complete the square on x
x^2 + [ (a^2 - 1) / a ] x = 1
x^2 + [ (a^2 - 1) / a ] x + (a^2 - 1)^2/ [4a^2] = 1 + (a^2 - 1)^2 / [4a^2 ]
(x + (a^2 - 1)/[2a] )^2 = [ 4a^2 + a^4 - 2a^2 + 1 ] / [ 4a^2]
(x + (a^2 - 1) / [2a] )^2 = [ a^4 + 2a^2 + 1] / [ 4a^2]
(x + (a^2 - 1) / [2a])^2 = [ a^2 + 1]^2 / [ 4a]^2 take both roots
( x + (a^2 - 1) / [2a] ) = ±√ [( a^2 + 1)^2 / [4a]^2]
x + (a^2-1) / [2a] = ± ( [ a^2 + 1] / [2a] )
x = ± ([a^2 + 1] / [2a]) - (a^2-1) /[2a ]
