(4x+1)/x=10/2x

Solution for (4x+1)/x=10/2x equation:

D( x )

x = 0

x = 0

x = 0

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

(4*x+1)/x = (10/2)*x // - (10/2)*x

(4*x+1)/x-((10/2)*x) = 0

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

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

4*x-5*x*x+1 = 0

4*x-5*x^2+1 = 0

4*x-5*x^2+1 = 0

4*x-5*x^2+1 = 0

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

DELTA = 36

DELTA > 0

x = (36^(1/2)-4)/(-5*2) or x = (-36^(1/2)-4)/(-5*2)

x = -1/5 or x = 1

(x+1/5)*(x-1) = 0

((x+1/5)*(x-1))/x = 0

((x+1/5)*(x-1))/x = 0 // * x

(x+1/5)*(x-1) = 0

( x+1/5 )

x+1/5 = 0 // - 1/5

x = -1/5

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -1/5, 1 }