Math equation

x - x^(-1) = 9/20
x^2 - 1 = 9x/20
20x^2 - 20 = 9x
20x^2 - 9x - 20 = 0
x = 5/4 or x = -4/5

so, x/2 + x^(-1/2)
= (5/4)/2 + (5/4)^(-1/2) or (-4/5)/2 + (-4/5)^(-1/2) (rejected)
= 5/8 + (4/5)^(1/2)

but i think the question is either
x^2 + [x^(-1)]^2 or x^(1/2) + x^(-1/2)

for x^2 + [x^(-1)]^2
= x^2 + 2x[x^(-1)] + [x^(-1)]^2 - 2x[x^(-1)]
= x^2 + 2x[x^(-1)] + [x^(-1)]^2 - 2
= [x + x^(-1)]^2 - 2
= (9/20)^2 - 2 = -719 / 400

for x^(1/2) + x^(-1/2)
= sqrt[x^(1/2) + x^(-1/2)]^2
= sqrt[x + 2x^(1/2)x^(-1/2) + x^(-1)]
= sqrt[x + 2 + x^(-1)]
= sqrt(9/20 + 2)
= sqrt(49/20) = 7sqrt5 / 10