8/(u-6)=(-5/(2u-12))+4

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Solution for 8/(u-6)=(-5/(2u-12))+4 equation: 


D( u )

u-6 = 0

2*u-12 = 0

u-6 = 0

u-6 = 0

u-6 = 0 // + 6

u = 6

2*u-12 = 0

2*u-12 = 0

2*u-12 = 0 // + 12

2*u = 12 // : 2

u = 12/2

u = 6

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

8/(u-6) = 4-5/(2*u-12) // - 4-5/(2*u-12)

8/(u-6)-(-5/(2*u-12))-4 = 0

8/(u-6)+5*(2*u-12)^-1-4 = 0

8/(u-6)+5/(2*u-12)-4 = 0

(8*(2*u-12))/((u-6)*(2*u-12))+(5*(u-6))/((u-6)*(2*u-12))+(-4*(u-6)*(2*u-12))/((u-6)*(2*u-12)) = 0

8*(2*u-12)+5*(u-6)-4*(u-6)*(2*u-12) = 0

21*u-8*u^2+96*u-288-126 = 0

117*u-8*u^2-414 = 0

117*u-8*u^2-414 = 0

117*u-8*u^2-414 = 0

DELTA = 117^2-(-414*(-8)*4)

DELTA = 441

DELTA > 0

u = (441^(1/2)-117)/(-8*2) or u = (-441^(1/2)-117)/(-8*2)

u = 6 or u = 69/8

(u-6)*(u-69/8) = 0

((u-6)*(u-69/8))/((u-6)*(2*u-12)) = 0

((u-6)*(u-69/8))/((u-6)*(2*u-12)) = 0 // * (u-6)*(2*u-12)

(u-6)*(u-69/8) = 0

( u-6 )

u-6 = 0 // + 6

u = 6

( u-69/8 )

u-69/8 = 0 // + 69/8

u = 69/8

u in { 6} 

u = 69/8

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