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

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Solution for (2x-1/2)/(4/5*x^2)=5/(2x-0,5) equation: 


D( x )

(4/5)*x^2 = 0

2*x-0.5 = 0

(4/5)*x^2 = 0

(4/5)*x^2 = 0

4/5*x^2 = 0 // : 4/5

x^2 = 0

x = 0

2*x-0.5 = 0

2*x-0.5 = 0

2*x-0.5 = 0 // + 0.5

2*x = 0.5 // : 2

x = 0.5/2

x = 0.25

x in (-oo:0) U (0:0.25) U (0.25:+oo)

(2*x-(1/2))/((4/5)*x^2) = 5/(2*x-0.5) // - 5/(2*x-0.5)

(2*x-(1/2))/((4/5)*x^2)-(5/(2*x-0.5)) = 0

(2*x-1/2)/((4/5)*x^2)-5*(2*x-0.5)^-1 = 0

(2*x-1/2)/(4/5*x^2)-5/(2*x-0.5) = 0

((2*x-1/2)*(2*x-0.5))/(4/5*x^2*(2*x-0.5))+(-5*4/5*x^2)/(4/5*x^2*(2*x-0.5)) = 0

(2*x-1/2)*(2*x-0.5)-5*4/5*x^2 = 0

0.25-2*x = 0

(0.25-2*x)/(4/5*x^2*(2*x-0.5)) = 0

(0.25-2*x)/(4/5*x^2*(2*x-0.5)) = 0 // * 4/5*x^2*(2*x-0.5)

0.25-2*x = 0

0.25-2*x = 0 // - 0.25

-2*x = -0.25 // : -2

x = -0.25/(-2)

x = 0.125

x = 0.125

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