6cos2x-14cos (в квадрате) x-7sin2x=0

6cos2x - 14cos²x - 7sin2x = 0

6cos²x - 6sin²x - 14cos²x - 14 sinx·cosx = 0

-8cos²x - 6sin²x - 14sinx·cosx = 0

4cos²x + 3sin²x + 7sinx·cosx = 0 : cos²x

4 + 3tg²x + 7tgx = 0

замена tgx = у

3 у² + 7 у + 4 = 0

D = 49 - 48 = 1

у1 = (-7 - 1) : 6 = - 4/3

у2 = (-7 + 1) : 6 = - 1

tgx1 = - 4/3

х1 = - arctg (4/3) + πk k∈Z

tgx2 = - 1

х1 = - π/4 + πk k∈Z