2tg²х + 3tgх - 2 = 0
Обозначим у = tgх и получим уравнение
2у² + 3у - 2 = 0
D = 3² - 4 · 2 · (-2) = 9 + 16 = 25; √25 = 5
y₁ = (-3 + 5) / (2 · 2) = 2/4 = 1/2
y₂ = (-3 - 5) / (2 · 2) = -8/4 = -2
tgх = 1/2, x = arctg(1/2) + πk, k ∈ Z
tgх = -2, х = -arctg2 + πn, n ∈ Z