3log^2√2x-14log√2x-5=0 помогите решить

Решение

3log^2√2x-14log√2x-5=0

ОДЗ: x > 0

log√2x = t

3t² - 14t - 5 = 0

D = 196 + 4*3*5 = 256

t₁ = (14 - 16) / 6 = - 1/3

t₂ = (14 + 16) / 6 = 5

1) log√2x = - 1/3

x = (√2) ⁻¹/³

x = 1 / (2) ¹/⁶

2) log√2x = 5

x = (√2) ⁵

x = √ (2⁵) = 4 √2