4x^0.5=x^-3/2

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Solution for 4x^0.5=x^-3/2 equation: 


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

4*x^0.5 = (x^-3)/2 // - (x^-3)/2

4*x^0.5-((x^-3)/2) = 0

4*x^0.5-1/2*x^-3 = 0

x^0.5*(4-1/2*x^-3.5) = 0

-1/2*x^-3.5 = -4 // : -1/2

x^-3.5 = 8

-3.5 < 0

1/(x^3.5) = 8 // * x^3.5

1 = 8*x^3.5 // : 8

1/8 = x^3.5

x^3 = (1/8)^(1/0.5) // ^ 1/3

x = 1/4

x^0.5 = 0

1*x^0.5 = 0 // : 1

x^0.5 = 0

x = 0

x in { 0} 

x = 1/4

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