(5)/(x+6)=-(3)/(2x+12)+1

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Solution for (5)/(x+6)=-(3)/(2x+12)+1 equation: 


D( x )

2*x+12 = 0

x+6 = 0

2*x+12 = 0

2*x+12 = 0

2*x+12 = 0 // - 12

2*x = -12 // : 2

x = -12/2

x = -6

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

x in (-oo:-6) U (-6:+oo)

5/(x+6) = 1-(3/(2*x+12)) // - 1-(3/(2*x+12))

5/(x+6)+3/(2*x+12)-1 = 0

(5*(2*x+12))/((x+6)*(2*x+12))+(3*(x+6))/((x+6)*(2*x+12))+(-1*(x+6)*(2*x+12))/((x+6)*(2*x+12)) = 0

5*(2*x+12)+3*(x+6)-1*(x+6)*(2*x+12) = 0

13*x-2*x^2-24*x-72+78 = 0

6-2*x^2-11*x = 0

6-2*x^2-11*x = 0

6-2*x^2-11*x = 0

DELTA = (-11)^2-(-2*4*6)

DELTA = 169

DELTA > 0

x = (169^(1/2)+11)/(-2*2) or x = (11-169^(1/2))/(-2*2)

x = -6 or x = 1/2

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

((x+6)*(x-1/2))/((x+6)*(2*x+12)) = 0

((x+6)*(x-1/2))/((x+6)*(2*x+12)) = 0 // * (x+6)*(2*x+12)

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

( x+6 )

x+6 = 0 // - 6

x = -6

( x-1/2 )

x-1/2 = 0 // + 1/2

x = 1/2

x in { -6} 

x = 1/2

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