4 sin^2x-5sinx×cosx-6cos^2x=0

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