7/(x+6)=x

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Solution for 7/(x+6)=x equation: 


D( x )

x+6 = 0

x+6 = 0

x+6 = 0

x+6 = 0 // - 6

x = -6

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

7/(x+6) = x // - x

7/(x+6)-x = 0

7/(x+6)+(-x*(x+6))/(x+6) = 0

7-x*(x+6) = 0

7-x^2-6*x = 0

7-x^2-6*x = 0

7-x^2-6*x = 0

DELTA = (-6)^2-(-1*4*7)

DELTA = 64

DELTA > 0

x = (64^(1/2)+6)/(-1*2) or x = (6-64^(1/2))/(-1*2)

x = -7 or x = 1

(x+7)*(x-1) = 0

((x+7)*(x-1))/(x+6) = 0

((x+7)*(x-1))/(x+6) = 0 // * x+6

(x+7)*(x-1) = 0

( x+7 )

x+7 = 0 // - 7

x = -7

( x-1 )

x-1 = 0 // + 1

x = 1

x in { -7, 1 }

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