x-8/x-5=5/4

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Solution for x-8/x-5=5/4 equation: 


D( x )

x = 0

x = 0

x = 0

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

x-(8/x)-5 = 5/4 // - 5/4

x-(8/x)-(5/4)-5 = 0

x-8*x^-1-5/4-5 = 0

1*x^1-8*x^-1-25/4*x^0 = 0

(1*x^2-25/4*x^1-8*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2-25/4*x^1-8*x^0) = 0

x^1

x^2+(-25/4)*x-8 = 0

x^2+(-25/4)*x-8 = 0

DELTA = (-25/4)^2-(-8*1*4)

DELTA = 1137/16

DELTA > 0

x = ((1137/16)^(1/2)-(-25/4))/(1*2) or x = (-(-25/4)-(1137/16)^(1/2))/(1*2)

x = ((1137/16)^(1/2)+25/4)/2 or x = (25/4-(1137/16)^(1/2))/2

x in { (25/4-(1137/16)^(1/2))/2, ((1137/16)^(1/2)+25/4)/2} 

x in { (25/4-(1137/16)^(1/2))/2, ((1137/16)^(1/2)+25/4)/2 }

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