Делим обе части на cos^2 x, имеем:
4 tg^2 x - 5 tg x - 6 = 0
tg x = t
4 t ^ 2 - 5 t - 6 = 0
D = 25 + 96 = 121
t = (5 +- 11) / 8
t1 = 2 t2 = - 3/4
tg x = 2 tg x = -3/4
x = arctg 2 + πn x = arctg (-3/4) + πn
(2x+9)/(3-2x)=(4x+3)/(5-4x)
(5-4x)(2x+9)=(3-2x)(4x+3)
-8x^2-26x+45=(3-2x)(4x+3)
-8x^2-26x+45=-8x^2+6x+9
36-32x=0
-4(8x-9)=0
8x-9=0
8x=9
x=9/8
Ответ: x=9/8