7/(5x-1)=1/4x

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Solution for 7/(5x-1)=1/4x equation:


D( x )

5*x-1 = 0

5*x-1 = 0

5*x-1 = 0

5*x-1 = 0 // + 1

5*x = 1 // : 5

x = 1/5

x in (-oo:1/5) U (1/5:+oo)

7/(5*x-1) = (1/4)*x // - (1/4)*x

7/(5*x-1)-((1/4)*x) = 0

7/(5*x-1)+(-1/4)*x = 0

7/(5*x-1)-x/4 = 0

(4*7)/(4*(5*x-1))+(-x*(5*x-1))/(4*(5*x-1)) = 0

4*7-x*(5*x-1) = 0

x-5*x^2+28 = 0

x-5*x^2+28 = 0

x-5*x^2+28 = 0

DELTA = 1^2-(-5*4*28)

DELTA = 561

DELTA > 0

x = (561^(1/2)-1)/(-5*2) or x = (-561^(1/2)-1)/(-5*2)

x = (561^(1/2)-1)/(-10) or x = (561^(1/2)+1)/10

(x-((561^(1/2)-1)/(-10)))*(x-((561^(1/2)+1)/10)) = 0

((x-((561^(1/2)-1)/(-10)))*(x-((561^(1/2)+1)/10)))/(4*(5*x-1)) = 0

((x-((561^(1/2)-1)/(-10)))*(x-((561^(1/2)+1)/10)))/(4*(5*x-1)) = 0 // * 4*(5*x-1)

(x-((561^(1/2)-1)/(-10)))*(x-((561^(1/2)+1)/10)) = 0

( x-((561^(1/2)+1)/10) )

x-((561^(1/2)+1)/10) = 0 // + (561^(1/2)+1)/10

x = (561^(1/2)+1)/10

( x-((561^(1/2)-1)/(-10)) )

x-((561^(1/2)-1)/(-10)) = 0 // + (561^(1/2)-1)/(-10)

x = (561^(1/2)-1)/(-10)

x in { (561^(1/2)+1)/10, (561^(1/2)-1)/(-10) }

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