5x=80x^-1/2

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Solution for 5x=80x^-1/2 equation: 


D( x )

x = 0

x = 0

x = 0

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

5*x = (80*x^-1)/2 // - (80*x^-1)/2

5*x-((80*x^-1)/2) = 0

5*x-40*x^-1 = 0

5*x^1-40*x^-1 = 0

(5*x^2-40*x^0)/(x^1) = 0 // * x^2

x^1*(5*x^2-40*x^0) = 0

x^1

5*x^2-40 = 0

5*x^2-40 = 0

DELTA = 0^2-(-40*4*5)

DELTA = 800

DELTA > 0

x = (800^(1/2)+0)/(2*5) or x = (0-800^(1/2))/(2*5)

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

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

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

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