6sin^2x+sin x cos x - cos^2x=2

6sin^2x+sin x cos x - cos^2x=2

6sin^2x+sin x cos x - cos^2x=2 (sin^2x+cos^2x)

6sin^2x+sin x cos x - cos^2x=2sin^2x+2cos^2x

6sin^2x+sin x cos x - cos^2x-2sin^2x-2cos^2x=0

4sin^2x+sin x cos x - 3cos^2x = 0 / : cos^2x≠0

4tg^2x+tgx-3 = 0

Замена tgx=t, t∈ (-∞; +∞)

4t^2+t-3 = 0

D=1+48=49

t = (-1+7) / 8=3/4

t = (-1-7) / 8 = - 8/8 = - 1

Получим:

tgx=3/4⇒ x=arctg (3/4) + pik, k∈Z

tgx = - 1⇒ x = - pi/4+pik, k∈Z