25^ (x-1,5) - 12*5^ (x-2) + 7=0

25^ (x-1,5) - 12*5^ (x-2) + 7 = 0

25^x : 25^ (3/2) - 12*5^x : 5^2 + 7 = 0

Замена 5^x = y > 0 при любом х

y^2 : 5^3 - 12*y : 5^2 + 7 = 0

Умножаем все на 5^3 = 125

y^2 - 12*5y + 7*125 = 0

y^2 - 60y + 875 = 0

D/4 = 30^2 - 875 = 900 - 875 = 25 = 5^2

y1 = 30 - 5 = 25 = 5^x; x1 = 2

y2 = 30 + 5 = 35 = 5^x; x2 = log_5 (35)