((5)/(9x+36))=((3)/(x+4))-((2)/(9))

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Solution for ((5)/(9x+36))=((3)/(x+4))-((2)/(9)) equation: 


D( x )

x+4 = 0

9*x+36 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

9*x+36 = 0

9*x+36 = 0

9*x+36 = 0 // - 36

9*x = -36 // : 9

x = -36/9

x = -4

x in (-oo:-4) U (-4:+oo)

5/(9*x+36) = 3/(x+4)-(2/9) // - 3/(x+4)-(2/9)

5/(9*x+36)-(3/(x+4))+2/9 = 0

5/(9*x+36)-3*(x+4)^-1+2/9 = 0

5/(9*x+36)-3/(x+4)+2/9 = 0

(5*9*(x+4))/(9*(9*x+36)*(x+4))+(-3*9*(9*x+36))/(9*(9*x+36)*(x+4))+(2*(9*x+36)*(x+4))/(9*(9*x+36)*(x+4)) = 0

5*9*(x+4)-3*9*(9*x+36)+2*(9*x+36)*(x+4) = 0

18*x^2-198*x+144*x-792+288 = 0

18*x^2-54*x-504 = 0

18*x^2-54*x-504 = 0

18*(x^2-3*x-28) = 0

x^2-3*x-28 = 0

DELTA = (-3)^2-(-28*1*4)

DELTA = 121

DELTA > 0

x = (121^(1/2)+3)/(1*2) or x = (3-121^(1/2))/(1*2)

x = 7 or x = -4

18*(x+4)*(x-7) = 0

(18*(x+4)*(x-7))/(9*(9*x+36)*(x+4)) = 0

(18*(x+4)*(x-7))/(9*(9*x+36)*(x+4)) = 0 // * 9*(9*x+36)*(x+4)

18*(x+4)*(x-7) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-7 )

x-7 = 0 // + 7

x = 7

x in { -4} 

x = 7

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