(5/2x)-(1/x)=6

Solution for (5/2x)-(1/x)=6 equation:

D( x )

x = 0

x = 0

x = 0

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

(5/2)*x-(1/x) = 6 // - 6

(5/2)*x-(1/x)-6 = 0

(5/2)*x-x^-1-6 = 0

5/2*x^1-1*x^-1-6*x^0 = 0

(5/2*x^2-6*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(5/2*x^2-6*x^1-1*x^0) = 0

x^1

(5/2)*x^2-6*x-1 = 0

(5/2)*x^2-6*x-1 = 0

DELTA = (-6)^2-(-1*4*(5/2))

DELTA = 46

DELTA > 0

x = (46^(1/2)+6)/(2*(5/2)) or x = (6-46^(1/2))/(2*(5/2))

x = (46^(1/2)+6)/5 or x = (6-46^(1/2))/5

x in { (6-46^(1/2))/5, (46^(1/2)+6)/5} 

x in { (6-46^(1/2))/5, (46^(1/2)+6)/5 }