5x^(8/5)=11x^(4/5)-2

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Solution for 5x^(8/5)=11x^(4/5)-2 equation: 


x in (-oo:+oo)

5*x^(8/5) = 11*x^(4/5)-2 // - 11*x^(4/5)-2

5*x^(8/5)-(11*x^(4/5))+2 = 0

5*x^(8/5)-11*x^(4/5)+2 = 0

t_1 = x^(4/5)

5*t_1^2-11*t_1^1+2 = 0

5*t_1^2-11*t_1+2 = 0

DELTA = (-11)^2-(2*4*5)

DELTA = 81

DELTA > 0

t_1 = (81^(1/2)+11)/(2*5) or t_1 = (11-81^(1/2))/(2*5)

t_1 = 2 or t_1 = 1/5

t_1 = 1/5

x^(4/5)-1/5 = 0

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

x^(4/5) = 1/5

x^(4/5) = 1/5 // ^ 5

x^4 = 1/3125 // ^ 1/4

abs(x) = (1/3125)^(1/4)

x = (1/3125)^(1/4) or x = -(1/3125)^(1/4)

t_1 = 2

x^(4/5)-2 = 0

1*x^(4/5) = 2 // : 1

x^(4/5) = 2

x^(4/5) = 2 // ^ 5

x^4 = 32 // ^ 1/4

abs(x) = 2*2^(1/4)

x = 2*2^(1/4) or x = -(2*2^(1/4))

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

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