eq = -0.45 - 8./(1 + 3 E^(-x/30)) + (80 E^(-x/30) (0.65 - 0.01 x))/(1 + 3 E^(-x/30))^2;
Solve[Rationalize[eq, 0] == 0, x, Reals]
(* {{x -> Root[{81 + 169 E^(#1/15) +
E^(#1/30) (-506 + 16 #1) &, -96.939605776733132399}]}, {x ->
Root[{81 + 169 E^(#1/15) + E^(#1/30) (-506 + 16 #1) &,
12.3348914426321591897}]}} *)
NSolve[eq == 0, x, Reals]
{{x -> -96.9396}, {x -> 12.3349}}
Or use FindRoot.
{FindRoot[eq, {x, 10}],FindRoot[eq, {x, -90}]}
(* {{x -> 12.3349}, {x -> -96.9396}} *)