(1/2x-8)-(3/x-4)=-5

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Solution for (1/2x-8)-(3/x-4)=-5 equation: 


D( x )

x = 0

x = 0

x = 0

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

(1/2)*x-(3/x)-8+4 = -5 // + 5

(1/2)*x-(3/x)-8+4+5 = 0

(1/2)*x-3*x^-1-8+4+5 = 0

1/2*x^1-3*x^-1+1*x^0 = 0

(1/2*x^2+1*x^1-3*x^0)/(x^1) = 0 // * x^2

x^1*(1/2*x^2+1*x^1-3*x^0) = 0

x^1

(1/2)*x^2+x-3 = 0

(1/2)*x^2+x-3 = 0

DELTA = 1^2-(-3*4*(1/2))

DELTA = 7

DELTA > 0

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

x = 7^(1/2)-1 or x = -(7^(1/2)+1)

x in { -(7^(1/2)+1), 7^(1/2)-1} 

x in { -(7^(1/2)+1), 7^(1/2)-1 }

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