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

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

D( x )

x = 0

x = 0

x = 0

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

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

(x-3)/2-(5/x) = 0

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

(x-3)/2-5/x = 0

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

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

x^2-3*x-10 = 0

x^2-3*x-10 = 0

x^2-3*x-10 = 0

DELTA = (-3)^2-(-10*1*4)

DELTA = 49

DELTA > 0

x = (49^(1/2)+3)/(1*2) or x = (3-49^(1/2))/(1*2)

x = 5 or x = -2

(x+2)*(x-5) = 0

((x+2)*(x-5))/(2*x) = 0

((x+2)*(x-5))/(2*x) = 0 // * 2*x

(x+2)*(x-5) = 0

( x+2 )

x+2 = 0 // - 2

x = -2

( x-5 )

x-5 = 0 // + 5

x = 5

x in { -2, 5 }