((5x)/(x+4))-((6)(x-3))=5

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Solution for ((5x)/(x+4))-((6)(x-3))=5 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)

(5*x)/(x+4)-(6*(x-3)) = 5 // - 5

(5*x)/(x+4)-(6*(x-3))-5 = 0

(5*x)/(x+4)-6*(x-3)-5 = 0

(5*x)/(x+4)+(-6*(x-3)*(x+4))/(x+4)+(-5*(x+4))/(x+4) = 0

5*x-6*(x-3)*(x+4)-5*(x+4) = 0

72-6*x^2-x-5*x-20 = 0

52-6*x^2-6*x = 0

52-6*x^2-6*x = 0

2*(26-3*x^2-3*x) = 0

26-3*x^2-3*x = 0

DELTA = (-3)^2-(-3*4*26)

DELTA = 321

DELTA > 0

x = (321^(1/2)+3)/(-3*2) or x = (3-321^(1/2))/(-3*2)

x = (321^(1/2)+3)/(-6) or x = (3-321^(1/2))/(-6)

2*(x-((321^(1/2)+3)/(-6)))*(x-((3-321^(1/2))/(-6))) = 0

(2*(x-((321^(1/2)+3)/(-6)))*(x-((3-321^(1/2))/(-6))))/(x+4) = 0

(2*(x-((321^(1/2)+3)/(-6)))*(x-((3-321^(1/2))/(-6))))/(x+4) = 0 // * x+4

2*(x-((321^(1/2)+3)/(-6)))*(x-((3-321^(1/2))/(-6))) = 0

( x-((3-321^(1/2))/(-6)) )

x-((3-321^(1/2))/(-6)) = 0 // + (3-321^(1/2))/(-6)

x = (3-321^(1/2))/(-6)

( x-((321^(1/2)+3)/(-6)) )

x-((321^(1/2)+3)/(-6)) = 0 // + (321^(1/2)+3)/(-6)

x = (321^(1/2)+3)/(-6)

x in { (3-321^(1/2))/(-6), (321^(1/2)+3)/(-6) }

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