4^x/4^x(2(5/2)^2x-(5/2)^x+1
(5/2)^x=t
f(t)=1/(2t^2-t+1)
f'(x)=-((4t-1)*(5/2)^xln(5/2))/(2t^2-t+1)^2
f'(x)=0
1-4t=0
t=1/4
2,5^x=0,25
x=log(5/2)1/4=ln1/4/ln(5/2)=-ln4/(ln5-ln2)~1,513
f(1/4)=1/(2*1/16-1/4+1)=1/(1/8-1/4+1)=1/(1-1/8)=8/7
max =8/7
x~-1,513