fx<-function(x) (0.501143 - 0.314445)*((1 + (0.716407*x)^1.574827)^(((1 - 1/1.574827) - 1) - 1)*(((1 - 1/1.574827) - 1)*((0.716407*x)^(1.574827 - 1)*(1.574827*0.716407)))*((1 - 1/1.574827)*((0.716407*x)^(1.574827 - 1)*(1.574827*0.716407))) + (1 + (0.716407*x)^1.574827)^((1 - 1/1.574827) - 1)*((1 - 1/1.574827)*((0.716407*x)^((1.574827 - 1) - 1)*((1.574827 - 1)*0.716407)*(1.574827*0.716407))))/((1 + (0.716407*x)^1.574827)^(1 - 1/1.574827))^2 - (0.501143 - 0.314445)*((1 + (0.716407*x)^1.574827)^((1 - 1/1.574827) - 1)*((1 - 1/1.574827)*((0.716407*x)^(1.574827 - 1)*(1.574827*0.716407))))*(2*((1 + (0.716407*x)^1.574827)^((1 - 1/1.574827) - 1)*((1 - 1/1.574827)*((0.716407*x)^(1.574827 - 1)*(1.574827*0.716407)))*((1 + (0.716407*x)^1.574827)^(1 - 1/1.574827))))/(((1 + (0.716407*x)^1.574827)^(1 - 1/1.574827))^2)^2
uniroot(fx,c(0,1))