Transfer Function from Differential Equation: X(s) / Y(s) Derivation

The transfer function form of this relationship is:

s^2 X(s) + 3.1s X(s) - 8.82 X(s) = 19.4 s^2 Y(s) + 36.2 s Y(s) + 1634 Y(s)

X(s) / Y(s) = (19.4 s^2 + 36.2 s + 1634) / (s^2 + 3.1s - 8.82)

where s is the Laplace variable.