1/x-4/5x=1

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 21/5

DELTA > 0

x = ((21/5)^(1/2)+1)/(2*(-4/5)) or x = (1-(21/5)^(1/2))/(2*(-4/5))

x = -5/8*((21/5)^(1/2)+1) or x = -5/8*(1-(21/5)^(1/2))

x in { -5/8*((21/5)^(1/2)+1), -5/8*(1-(21/5)^(1/2))} 

x in { -5/8*((21/5)^(1/2)+1), -5/8*(1-(21/5)^(1/2)) }

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