9x^(6/5)=18x^(3/5)-8

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Solution for 9x^(6/5)=18x^(3/5)-8 equation: 


x in (-oo:+oo)

9*x^(6/5) = 18*x^(3/5)-8 // - 18*x^(3/5)-8

9*x^(6/5)-(18*x^(3/5))+8 = 0

9*x^(6/5)-18*x^(3/5)+8 = 0

t_1 = x^(3/5)

9*t_1^2-18*t_1^1+8 = 0

9*t_1^2-18*t_1+8 = 0

DELTA = (-18)^2-(4*8*9)

DELTA = 36

DELTA > 0

t_1 = (36^(1/2)+18)/(2*9) or t_1 = (18-36^(1/2))/(2*9)

t_1 = 4/3 or t_1 = 2/3

t_1 = 2/3

x^(3/5)-2/3 = 0

1*x^(3/5) = 2/3 // : 1

x^(3/5) = 2/3

x^(3/5) = 2/3 // ^ 5

x^3 = 32/243 // ^ 1/3

x = (32/243)^(1/3)

t_1 = 4/3

x^(3/5)-4/3 = 0

1*x^(3/5) = 4/3 // : 1

x^(3/5) = 4/3

x^(3/5) = 4/3 // ^ 5

x^3 = 1024/243 // ^ 1/3

x = (1024/243)^(1/3)

x in { (32/243)^(1/3), (1024/243)^(1/3) }

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