12x^(-2/5)-19x^(-1/5)-11=0

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Solution for 12x^(-2/5)-19x^(-1/5)-11=0 equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

12*x^(-2/5)-(19*x^(-1/5))-11 = 0

12*x^(-2/5)-19*x^(-1/5)-11 = 0

t_1 = x^(-1/5)

12*t_1^2-19*t_1^1-11 = 0

12*t_1^2-19*t_1-11 = 0

DELTA = (-19)^2-(-11*4*12)

DELTA = 889

DELTA > 0

t_1 = (889^(1/2)+19)/(2*12) or t_1 = (19-889^(1/2))/(2*12)

t_1 = (889^(1/2)+19)/24 or t_1 = (19-889^(1/2))/24

t_1 = (19-889^(1/2))/24

x^(-1/5)-((19-889^(1/2))/24) = 0

1*x^(-1/5) = (19-889^(1/2))/24 // : 1

x^(-1/5) = (19-889^(1/2))/24

-1/5 < 0

1/(x^(1/5)) = (19-889^(1/2))/24 // * x^(1/5)

1 = ((19-889^(1/2))/24)*x^(1/5) // : (19-889^(1/2))/24

24*(19-889^(1/2))^-1 = x^(1/5)

x^(1/5) = 24*(19-889^(1/2))^-1 // ^ 5

x = 7962624*(19-889^(1/2))^-5

t_1 = (889^(1/2)+19)/24

x^(-1/5)-((889^(1/2)+19)/24) = 0

1*x^(-1/5) = (889^(1/2)+19)/24 // : 1

x^(-1/5) = (889^(1/2)+19)/24

-1/5 < 0

1/(x^(1/5)) = (889^(1/2)+19)/24 // * x^(1/5)

1 = ((889^(1/2)+19)/24)*x^(1/5) // : (889^(1/2)+19)/24

24*(889^(1/2)+19)^-1 = x^(1/5)

x^(1/5) = 24*(889^(1/2)+19)^-1 // ^ 5

x = 0

x in { 0} 

x = 7962624*(19-889^(1/2))^-5

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