4*2^2x -(2*3)^x = 18*3^2x | : 2^2x
4 - (3/2)^x = 18*(3/2)^2x
(3/2)^x = t
4 -t -18t^2 = 0
18t^2 +t - 4 = 0
D = b^2 -4ac = 1 +288 = 289
t1= (-1 +17)/36 = 16/36 = 4/9
t2 = (-1 -17)/36 = -18/36
а)t=4/9
(3/2)^x = 4/9
х = -2
б) t = -18/36
(3/2)^x = -18/36
нет решений.
Ответ: -2