5x^0.5=0.2x^-3/2

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Solution for 5x^0.5=0.2x^-3/2 equation: 


D( x )

x < 0

x = 0

x < 0

x = 0

x = 0

x in (0:+oo)

5*x^0.5 = (0.2*x^-3)/2 // - (0.2*x^-3)/2

5*x^0.5-((0.2*x^-3)/2) = 0

5*x^0.5-0.1*x^-3 = 0

5*x^0.5-0.1*x^-3 = 0

x^0.5*(5-0.1*x^-3.5) = 0

-0.1*x^-3.5 = -5 // : -0.1

x^-3.5 = 50

-3.5 < 0

1/(x^3.5) = 50 // * x^3.5

1 = 50*x^3.5 // : 50

1/50 = x^3.5

x^3 = (1/50)^(1/0.5) // ^ 1/3

x = (1/2500)^(1/3)

x^0.5 = 0

1*x^0.5 = 0 // : 1

x^0.5 = 0

x = 0

x in { 0} 

x = (1/2500)^(1/3)

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