3x/5+13/x=8/x+4

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Solution for 3x/5+13/x=8/x+4 equation: 


D( x )

x = 0

x = 0

x = 0

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

(3*x)/5+13/x = 8/x+4 // - 8/x+4

(3*x)/5+13/x-(8/x)-4 = 0

(3*x)/5+13/x-8*x^-1-4 = 0

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

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

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

x^1

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

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

DELTA = (-4)^2-(4*5*(3/5))

DELTA = 4

DELTA > 0

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

x = 5 or x = 5/3

x in { 5/3, 5} 

x in { 5/3, 5 }

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