X-4/x-5=6/5-x

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Solution for X-4/x-5=6/5-x equation: 


D( x )

x = 0

x = 0

x = 0

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

X-(4/x)-5 = 6/5-x // - 6/5-x

X+x-(4/x)-(6/5)-5 = 0

X+x-4*x^-1-6/5-5 = 0

1*x^1-4*x^-1-31/5*x^0 = 0

(1*x^2-31/5*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-31/5*x^1-4*x^0) = 0

x^1

x^2+(-31/5)*x-4 = 0

x^2+(-31/5)*x-4 = 0

DELTA = (-31/5)^2-(-4*1*4)

DELTA = 1361/25

DELTA > 0

x = ((1361/25)^(1/2)-(-31/5))/(1*2) or x = (-(-31/5)-(1361/25)^(1/2))/(1*2)

x = ((1361/25)^(1/2)+31/5)/2 or x = (31/5-(1361/25)^(1/2))/2

x in { (31/5-(1361/25)^(1/2))/2, ((1361/25)^(1/2)+31/5)/2} 

x in { (31/5-(1361/25)^(1/2))/2, ((1361/25)^(1/2)+31/5)/2 }

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