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