(1/(7x+28))=(3/(x+4))-(4/7)

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Solution for (1/(7x+28))=(3/(x+4))-(4/7) equation: 


D( x )

x+4 = 0

7*x+28 = 0

x+4 = 0

x+4 = 0

x+4 = 0 // - 4

x = -4

7*x+28 = 0

7*x+28 = 0

7*x+28 = 0 // - 28

7*x = -28 // : 7

x = -28/7

x = -4

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

1/(7*x+28) = 3/(x+4)-(4/7) // - 3/(x+4)-(4/7)

1/(7*x+28)-(3/(x+4))+4/7 = 0

1/(7*x+28)-3*(x+4)^-1+4/7 = 0

1/(7*x+28)-3/(x+4)+4/7 = 0

(1*7*(x+4))/(7*(7*x+28)*(x+4))+(-3*7*(7*x+28))/(7*(7*x+28)*(x+4))+(4*(7*x+28)*(x+4))/(7*(7*x+28)*(x+4)) = 0

1*7*(x+4)-3*7*(7*x+28)+4*(7*x+28)*(x+4) = 0

28*x^2-140*x+224*x-560+448 = 0

28*x^2+84*x-112 = 0

28*x^2+84*x-112 = 0

28*(x^2+3*x-4) = 0

x^2+3*x-4 = 0

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

DELTA = 25

DELTA > 0

x = (25^(1/2)-3)/(1*2) or x = (-25^(1/2)-3)/(1*2)

x = 1 or x = -4

28*(x+4)*(x-1) = 0

(28*(x+4)*(x-1))/(7*(7*x+28)*(x+4)) = 0

(28*(x+4)*(x-1))/(7*(7*x+28)*(x+4)) = 0 // * 7*(7*x+28)*(x+4)

28*(x+4)*(x-1) = 0

( x+4 )

x+4 = 0 // - 4

x = -4

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -4} 

x = 1

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