(5/x)-(3/1)=(10/2x)

Solution for (5/x)-(3/1)=(10/2x) equation:

D( x )

x = 0

x = 0

x = 0

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

5/x-(3/1) = (10/2)*x // - (10/2)*x

5/x-((10/2)*x)-(3/1) = 0

5/x-5*x-3 = 0

5*x^-1-5*x^1-3*x^0 = 0

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

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

x^1

5-5*x^2-3*x = 0

5-5*x^2-3*x = 0

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

DELTA = 109

DELTA > 0

x = (109^(1/2)+3)/(-5*2) or x = (3-109^(1/2))/(-5*2)

x = (109^(1/2)+3)/(-10) or x = (3-109^(1/2))/(-10)

x in { (109^(1/2)+3)/(-10), (3-109^(1/2))/(-10)} 

x in { (109^(1/2)+3)/(-10), (3-109^(1/2))/(-10) }