find the the 2nd derivative and set equal to zero in order to find inflection points of the function

f(x)=1/(5x^2+4)

I would write it as

f(x) = (5x^2 + 4)^-1

f'(x) = -(5x^2 + 4)^-2 (10x)
= -10x(5x^2 + 4)^-2

f''(x) = -10x(-2)(5x^2 + 4)^-3 (10x) - 10(5x^2 + 4)^-2
= -10(5x^2 + 4)^-3 [ 10x^2 + 5x^2 + 4 ]

can you set this equal to zero and solve?

check my arithmetic.