1) √(5x+1) = 2x - 8
4x - 16 = √(5x + 1)
(4x - 16)^2 = 5x + 1
16x^2 - 128x + 256 = 5x + 1
16x^2 - 133x + 255 = 0

Решаем квадратное уравнение:
D = b^2 - 4ac
D = (-133)^2 - 416255
D = 17689 - 16320
D = 1369

x1 = (-(-133) + √1369) / 32 = (133 + 37) / 32 = 170 / 32 = 5.3125
x2 = (-(-133) - √1369) / 32 = (133 - 37) / 32 = 96 / 32 = 3

Ответ: x1 = 5.3125, x2 = 3

2) x^6 - 9x^4 - 9x^2 + 81 = 0
Решаем это уравнение как квадратное уравнение относительно x^2:
(x^2)^3 - 9(x^2)^2 - 9x^2 + 81 = 0
Let y = x^2:
y^3 - 9y^2 - 9y + 81 = 0

y = 3 is a root:
3^3 - 93^2 - 93 + 81 = 27 - 81 - 27 + 81 = 0

(y - 3)(y^2 - 6y - 27) = 0
(y - 3)(y - 9)(y + 3) = 0

y1 = 3, y2 = 9, y3 = -3

x^2 = 3, x^2 = 9, x^2 = -3
x = ±√3, x = ±3i, x = ±√3i

Ответ: x = ±√3, x = ±3i, x = ±√3i