2/(5w-30)+2=6/(w-6)

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Solution for 2/(5w-30)+2=6/(w-6) equation: 


D( w )

5*w-30 = 0

w-6 = 0

5*w-30 = 0

5*w-30 = 0

5*w-30 = 0 // + 30

5*w = 30 // : 5

w = 30/5

w = 6

w-6 = 0

w-6 = 0

w-6 = 0 // + 6

w = 6

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

2/(5*w-30)+2 = 6/(w-6) // - 6/(w-6)

2/(5*w-30)-(6/(w-6))+2 = 0

2/(5*w-30)-6*(w-6)^-1+2 = 0

2/(5*w-30)-6/(w-6)+2 = 0

(2*(w-6))/((5*w-30)*(w-6))+(-6*(5*w-30))/((5*w-30)*(w-6))+(2*(5*w-30)*(w-6))/((5*w-30)*(w-6)) = 0

2*(w-6)-6*(5*w-30)+2*(5*w-30)*(w-6) = 0

10*w^2-28*w-120*w+168+360 = 0

10*w^2-148*w+528 = 0

10*w^2-148*w+528 = 0

2*(5*w^2-74*w+264) = 0

5*w^2-74*w+264 = 0

DELTA = (-74)^2-(4*5*264)

DELTA = 196

DELTA > 0

w = (196^(1/2)+74)/(2*5) or w = (74-196^(1/2))/(2*5)

w = 44/5 or w = 6

2*(w-6)*(w-44/5) = 0

(2*(w-6)*(w-44/5))/((5*w-30)*(w-6)) = 0

(2*(w-6)*(w-44/5))/((5*w-30)*(w-6)) = 0 // * (5*w-30)*(w-6)

2*(w-6)*(w-44/5) = 0

( w-44/5 )

w-44/5 = 0 // + 44/5

w = 44/5

( w-6 )

w-6 = 0 // + 6

w = 6

w in { 6} 

w = 44/5

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