5x^(6/5)=14x^(3/5)-8

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Solution for 5x^(6/5)=14x^(3/5)-8 equation: 


x in (-oo:+oo)

5*x^(6/5) = 14*x^(3/5)-8 // - 14*x^(3/5)-8

5*x^(6/5)-(14*x^(3/5))+8 = 0

5*x^(6/5)-14*x^(3/5)+8 = 0

t_1 = x^(3/5)

5*t_1^2-14*t_1^1+8 = 0

5*t_1^2-14*t_1+8 = 0

DELTA = (-14)^2-(4*5*8)

DELTA = 36

DELTA > 0

t_1 = (36^(1/2)+14)/(2*5) or t_1 = (14-36^(1/2))/(2*5)

t_1 = 2 or t_1 = 4/5

t_1 = 4/5

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

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

x^(3/5) = 4/5

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

x^3 = 1024/3125 // ^ 1/3

x = (1024/3125)^(1/3)

t_1 = 2

x^(3/5)-2 = 0

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

x^(3/5) = 2

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

x^3 = 32 // ^ 1/3

x = 2*4^(1/3)

x in { (1024/3125)^(1/3), 2*4^(1/3) }

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