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

3у² + 7у + 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