Все слагаемые разделим на 15^x > 0;
25* 9^x / 15^x - 34* 15^x / 15^x + 9* 25^x / 15^x = 0;
25 * (3/5)^x - 34 * 1 + 9* (5/3)^x = 0;
(3/5)^x = t > 0;
(5/3)^x = 1/t;
25* t - 34 + 9 / t = 0; *t;
25t^2 - 34 t + 9 = 0;
D = 34^2 - 4*25*9 = 1156 - 900 = 256= 16^2;
t1 =(34+16) / 50 = 1; ⇒ (3/5)^x = 1; x = 0.
t2 = (34 - 16) / 50 = 18/50 = 9/25; ⇒ (3/5)^x = 9/25; (3/5)^x = (3/5)^2 ; x = 2
Ответ: х =0 или х =2