x-3/5x-24=1/x-4

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Solution for x-3/5x-24=1/x-4 equation:


D( x )

x = 0

x = 0

x = 0

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

x-((3/5)*x)-24 = 1/x-4 // - 1/x-4

x-((3/5)*x)-(1/x)-24+4 = 0

x+(-3/5)*x-x^-1-24+4 = 0

2/5*x^1-1*x^-1-20*x^0 = 0

(2/5*x^2-20*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(2/5*x^2-20*x^1-1*x^0) = 0

x^1

(2/5)*x^2-20*x-1 = 0

(2/5)*x^2-20*x-1 = 0

DELTA = (-20)^2-(-1*4*(2/5))

DELTA = 2008/5

DELTA > 0

x = ((2008/5)^(1/2)+20)/(2*(2/5)) or x = (20-(2008/5)^(1/2))/(2*(2/5))

x = 5/4*((2008/5)^(1/2)+20) or x = 5/4*(20-(2008/5)^(1/2))

x in { 5/4*(20-(2008/5)^(1/2)), 5/4*((2008/5)^(1/2)+20)}

x in { 5/4*(20-(2008/5)^(1/2)), 5/4*((2008/5)^(1/2)+20) }

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