7/(5x-2)=5/4x

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Solution for 7/(5x-2)=5/4x equation: 


D( x )

5*x-2 = 0

5*x-2 = 0

5*x-2 = 0

5*x-2 = 0 // + 2

5*x = 2 // : 5

x = 2/5

x in (-oo:2/5) U (2/5:+oo)

7/(5*x-2) = (5/4)*x // - (5/4)*x

7/(5*x-2)-((5/4)*x) = 0

7/(5*x-2)+(-5/4)*x = 0

7/(5*x-2)+(-5*x)/4 = 0

(4*7)/(4*(5*x-2))+(-5*x*(5*x-2))/(4*(5*x-2)) = 0

4*7-5*x*(5*x-2) = 0

10*x-25*x^2+28 = 0

10*x-25*x^2+28 = 0

10*x-25*x^2+28 = 0

DELTA = 10^2-(-25*4*28)

DELTA = 2900

DELTA > 0

x = (2900^(1/2)-10)/(-25*2) or x = (-2900^(1/2)-10)/(-25*2)

x = (10*29^(1/2)-10)/(-50) or x = (-10*29^(1/2)-10)/(-50)

(x-((10*29^(1/2)-10)/(-50)))*(x-((-10*29^(1/2)-10)/(-50))) = 0

((x-((10*29^(1/2)-10)/(-50)))*(x-((-10*29^(1/2)-10)/(-50))))/(4*(5*x-2)) = 0

((x-((10*29^(1/2)-10)/(-50)))*(x-((-10*29^(1/2)-10)/(-50))))/(4*(5*x-2)) = 0 // * 4*(5*x-2)

(x-((10*29^(1/2)-10)/(-50)))*(x-((-10*29^(1/2)-10)/(-50))) = 0

( x-((-10*29^(1/2)-10)/(-50)) )

x-((-10*29^(1/2)-10)/(-50)) = 0 // + (-10*29^(1/2)-10)/(-50)

x = (-10*29^(1/2)-10)/(-50)

( x-((10*29^(1/2)-10)/(-50)) )

x-((10*29^(1/2)-10)/(-50)) = 0 // + (10*29^(1/2)-10)/(-50)

x = (10*29^(1/2)-10)/(-50)

x in { (-10*29^(1/2)-10)/(-50), (10*29^(1/2)-10)/(-50) }

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