5/(2w+12)+1=-8/(w+6)

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Solution for 5/(2w+12)+1=-8/(w+6) equation: 


D( w )

w+6 = 0

2*w+12 = 0

w+6 = 0

w+6 = 0

w+6 = 0 // - 6

w = -6

2*w+12 = 0

2*w+12 = 0

2*w+12 = 0 // - 12

2*w = -12 // : 2

w = -12/2

w = -6

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

5/(2*w+12)+1 = -8/(w+6) // + -8/(w+6)

5/(2*w+12)-(-8/(w+6))+1 = 0

5/(2*w+12)+8*(w+6)^-1+1 = 0

5/(2*w+12)+8/(w+6)+1 = 0

(5*(w+6))/((2*w+12)*(w+6))+(8*(2*w+12))/((2*w+12)*(w+6))+(1*(2*w+12)*(w+6))/((2*w+12)*(w+6)) = 0

5*(w+6)+8*(2*w+12)+1*(2*w+12)*(w+6) = 0

2*w^2+21*w+24*w+72+126 = 0

2*w^2+45*w+198 = 0

2*w^2+45*w+198 = 0

2*w^2+45*w+198 = 0

DELTA = 45^2-(2*4*198)

DELTA = 441

DELTA > 0

w = (441^(1/2)-45)/(2*2) or w = (-441^(1/2)-45)/(2*2)

w = -6 or w = -33/2

(w+33/2)*(w+6) = 0

((w+33/2)*(w+6))/((2*w+12)*(w+6)) = 0

((w+33/2)*(w+6))/((2*w+12)*(w+6)) = 0 // * (2*w+12)*(w+6)

(w+33/2)*(w+6) = 0

( w+33/2 )

w+33/2 = 0 // - 33/2

w = -33/2

( w+6 )

w+6 = 0 // - 6

w = -6

w in { -6} 

w = -33/2

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