x-5/x-7=4/7-x

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Solution for x-5/x-7=4/7-x equation: 


D( x )

x = 0

x = 0

x = 0

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

x-(5/x)-7 = 4/7-x // - 4/7-x

x+x-(5/x)-(4/7)-7 = 0

x+x-5*x^-1-4/7-7 = 0

2*x^1-5*x^-1-53/7*x^0 = 0

(2*x^2-53/7*x^1-5*x^0)/(x^1) = 0 // * x^2

x^1*(2*x^2-53/7*x^1-5*x^0) = 0

x^1

2*x^2+(-53/7)*x-5 = 0

2*x^2+(-53/7)*x-5 = 0

DELTA = (-53/7)^2-(-5*2*4)

DELTA = 4769/49

DELTA > 0

x = ((4769/49)^(1/2)-(-53/7))/(2*2) or x = (-(-53/7)-(4769/49)^(1/2))/(2*2)

x = ((4769/49)^(1/2)+53/7)/4 or x = (53/7-(4769/49)^(1/2))/4

x in { (53/7-(4769/49)^(1/2))/4, ((4769/49)^(1/2)+53/7)/4} 

x in { (53/7-(4769/49)^(1/2))/4, ((4769/49)^(1/2)+53/7)/4 }

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