5/(2x+3)+8/(x-6)=1

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Solution for 5/(2x+3)+8/(x-6)=1 equation: 


D( x )

x-6 = 0

2*x+3 = 0

x-6 = 0

x-6 = 0

x-6 = 0 // + 6

x = 6

2*x+3 = 0

2*x+3 = 0

2*x+3 = 0 // - 3

2*x = -3 // : 2

x = -3/2

x in (-oo:-3/2) U (-3/2:6) U (6:+oo)

5/(2*x+3)+8/(x-6) = 1 // - 1

5/(2*x+3)+8/(x-6)-1 = 0

(5*(x-6))/((2*x+3)*(x-6))+(8*(2*x+3))/((2*x+3)*(x-6))+(-1*(2*x+3)*(x-6))/((2*x+3)*(x-6)) = 0

5*(x-6)+8*(2*x+3)-1*(2*x+3)*(x-6) = 0

21*x-2*x^2+9*x-6+18 = 0

30*x-2*x^2+12 = 0

30*x-2*x^2+12 = 0

2*(15*x-x^2+6) = 0

15*x-x^2+6 = 0

DELTA = 15^2-(-1*4*6)

DELTA = 249

DELTA > 0

x = (249^(1/2)-15)/(-1*2) or x = (-249^(1/2)-15)/(-1*2)

x = (249^(1/2)-15)/(-2) or x = (249^(1/2)+15)/2

2*(x-((249^(1/2)-15)/(-2)))*(x-((249^(1/2)+15)/2)) = 0

(2*(x-((249^(1/2)-15)/(-2)))*(x-((249^(1/2)+15)/2)))/((2*x+3)*(x-6)) = 0

(2*(x-((249^(1/2)-15)/(-2)))*(x-((249^(1/2)+15)/2)))/((2*x+3)*(x-6)) = 0 // * (2*x+3)*(x-6)

2*(x-((249^(1/2)-15)/(-2)))*(x-((249^(1/2)+15)/2)) = 0

( x-((249^(1/2)+15)/2) )

x-((249^(1/2)+15)/2) = 0 // + (249^(1/2)+15)/2

x = (249^(1/2)+15)/2

( x-((249^(1/2)-15)/(-2)) )

x-((249^(1/2)-15)/(-2)) = 0 // + (249^(1/2)-15)/(-2)

x = (249^(1/2)-15)/(-2)

x in { (249^(1/2)+15)/2, (249^(1/2)-15)/(-2) }

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