2x-1/5=4/x

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Solution for 2x-1/5=4/x equation: 


D( x )

x = 0

x = 0

x = 0

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

2*x-(1/5) = 4/x // - 4/x

2*x-(4/x)-(1/5) = 0

2*x-4*x^-1-1/5 = 0

2*x^1-4*x^-1-1/5*x^0 = 0

(2*x^2-1/5*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(2*x^2-1/5*x^1-4*x^0) = 0

x^1

2*x^2+(-1/5)*x-4 = 0

2*x^2+(-1/5)*x-4 = 0

DELTA = (-1/5)^2-(-4*2*4)

DELTA = 801/25

DELTA > 0

x = ((801/25)^(1/2)-(-1/5))/(2*2) or x = (-(-1/5)-(801/25)^(1/2))/(2*2)

x = ((801/25)^(1/2)+1/5)/4 or x = (1/5-(801/25)^(1/2))/4

x in { (1/5-(801/25)^(1/2))/4, ((801/25)^(1/2)+1/5)/4} 

x in { (1/5-(801/25)^(1/2))/4, ((801/25)^(1/2)+1/5)/4 }

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