6/(x-7)=4x

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Solution for 6/(x-7)=4x equation: 


D( x )

x-7 = 0

x-7 = 0

x-7 = 0

x-7 = 0 // + 7

x = 7

x in (-oo:7) U (7:+oo)

6/(x-7) = 4*x // - 4*x

6/(x-7)-(4*x) = 0

6/(x-7)-4*x = 0

6/(x-7)+(-4*x*(x-7))/(x-7) = 0

6-4*x*(x-7) = 0

28*x-4*x^2+6 = 0

28*x-4*x^2+6 = 0

2*(14*x-2*x^2+3) = 0

14*x-2*x^2+3 = 0

DELTA = 14^2-(-2*3*4)

DELTA = 220

DELTA > 0

x = (220^(1/2)-14)/(-2*2) or x = (-220^(1/2)-14)/(-2*2)

x = (2*55^(1/2)-14)/(-4) or x = (-2*55^(1/2)-14)/(-4)

2*(x-((2*55^(1/2)-14)/(-4)))*(x-((-2*55^(1/2)-14)/(-4))) = 0

(2*(x-((2*55^(1/2)-14)/(-4)))*(x-((-2*55^(1/2)-14)/(-4))))/(x-7) = 0

(2*(x-((2*55^(1/2)-14)/(-4)))*(x-((-2*55^(1/2)-14)/(-4))))/(x-7) = 0 // * x-7

2*(x-((2*55^(1/2)-14)/(-4)))*(x-((-2*55^(1/2)-14)/(-4))) = 0

( x-((-2*55^(1/2)-14)/(-4)) )

x-((-2*55^(1/2)-14)/(-4)) = 0 // + (-2*55^(1/2)-14)/(-4)

x = (-2*55^(1/2)-14)/(-4)

( x-((2*55^(1/2)-14)/(-4)) )

x-((2*55^(1/2)-14)/(-4)) = 0 // + (2*55^(1/2)-14)/(-4)

x = (2*55^(1/2)-14)/(-4)

x in { (-2*55^(1/2)-14)/(-4), (2*55^(1/2)-14)/(-4) }

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