(3/5)*5^(2x) - (50/25)*5^(x) = 1/5 - домножим обе части на 5
3*5^(2x) - 10*5^x = 1
Замена: 5^(x) = t > 0
3t^2 - 10t - 1 = 0
D = 100 + 12 = 112 = 4*25*2
t1 = (10 - 10sqrt2)/6 = (5 - 5sqrt2)/3 < 0 - посторонний корень
t2 = (10 + 10sqrt2)/6 = (5 + 5sqrt2)/3 > 0 - корень
5^x = (5 + 5sqrt2)/3
x = log5((5 + 5sqrt2)/3)