9x^(6/5)=15x^(3/5)-4

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Solution for 9x^(6/5)=15x^(3/5)-4 equation: 


x in (-oo:+oo)

9*x^(6/5) = 15*x^(3/5)-4 // - 15*x^(3/5)-4

9*x^(6/5)-(15*x^(3/5))+4 = 0

9*x^(6/5)-15*x^(3/5)+4 = 0

t_1 = x^(3/5)

9*t_1^2-15*t_1^1+4 = 0

9*t_1^2-15*t_1+4 = 0

DELTA = (-15)^2-(4*4*9)

DELTA = 81

DELTA > 0

t_1 = (81^(1/2)+15)/(2*9) or t_1 = (15-81^(1/2))/(2*9)

t_1 = 4/3 or t_1 = 1/3

t_1 = 1/3

x^(3/5)-1/3 = 0

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

x^(3/5) = 1/3

x^(3/5) = 1/3 // ^ 5

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

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

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