9(x/2 + 5/6)^4 + 14(x/2 + 5/6)^2 - 8 = 0

Question

9(x/2 + 5/6)^4 + 14(x/2 + 5/6)^2 - 8 = 0

Answer 1

( X/2 + 5/6 )^2 = a ; a > 0
9a^2 + 14a - 8 = 0
D = 196 + 288 = 484 = 22^2
a1 = ( - 14 + 22 ) : 18 =8/18 = 4/9
a2 = ( - 14 - 22 ) : 18 = - 2 ; < 0
( X/2 + 5/6 )^2 = 4/9
X/2 + 5/6 = 2/3
6x + 5 = 4
X = - 1/6