Implicit Root and RegionPlot

Question

Here is my problem:

I am trying to RegionPlot; however, I have an implicit root. I tried the following code but it generates an error and does not paint the region I know for sure exits: ""The function value {0.495021 -0.0000602472\ d} is not a list of \ numbers with dimensions {1} at {[Gamma]t} = {0.1}. ""

T he code is:

  bigG2[Qb_, d_, α_, μ_, c_] := FindRoot[1/2 (1 + α (-1 + γt)^2 - γt^2) - (
d Qb (α + γt - α γt))/(
c + α (-1 + γt) μ) == 0, {γt, 1/10}][[1, 2]]


bigF2[Qb_, d_, α_, μ_, c_] :=c - d bigG2[Qb, d, α, μ,c] - α (1 - bigG2[Qb, d, α, μ, c]) (d + μ)

var = {μ -> 1, d -> 40/100, c -> 35/100}

RegionPlot[{bigF2[Qb, d, α /. var, μ /. var, c /. var] < 
 0 && (α μ)/(1 - α) < c && 
Qb < ((1 + α) (c - α μ))/(2 d α) /. var}, {Qb, 0, 4}, {α, 0, 1 /. var}] 

Any help is appreciated.