(1/(x-4))+1=(14(x+2))

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Solution for (1/(x-4))+1=(14(x+2)) equation:


D( x )

x-4 = 0

x-4 = 0

x-4 = 0

x-4 = 0 // + 4

x = 4

x in (-oo:4) U (4:+oo)

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

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

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

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

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

28*x-14*x^2+x-4+113 = 0

29*x-14*x^2+109 = 0

29*x-14*x^2+109 = 0

29*x-14*x^2+109 = 0

DELTA = 29^2-(-14*4*109)

DELTA = 6945

DELTA > 0

x = (6945^(1/2)-29)/(-14*2) or x = (-6945^(1/2)-29)/(-14*2)

x = (6945^(1/2)-29)/(-28) or x = (6945^(1/2)+29)/28

(x-((6945^(1/2)-29)/(-28)))*(x-((6945^(1/2)+29)/28)) = 0

((x-((6945^(1/2)-29)/(-28)))*(x-((6945^(1/2)+29)/28)))/(x-4) = 0

((x-((6945^(1/2)-29)/(-28)))*(x-((6945^(1/2)+29)/28)))/(x-4) = 0 // * x-4

(x-((6945^(1/2)-29)/(-28)))*(x-((6945^(1/2)+29)/28)) = 0

( x-((6945^(1/2)+29)/28) )

x-((6945^(1/2)+29)/28) = 0 // + (6945^(1/2)+29)/28

x = (6945^(1/2)+29)/28

( x-((6945^(1/2)-29)/(-28)) )

x-((6945^(1/2)-29)/(-28)) = 0 // + (6945^(1/2)-29)/(-28)

x = (6945^(1/2)-29)/(-28)

x in { (6945^(1/2)+29)/28, (6945^(1/2)-29)/(-28) }

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