X^2+9x+6/(x+6)

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Solution for X^2+9x+6/(x+6) 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)

t_1 = X^2

6/(x+6)+t_1+9*x = 0

6/(x+6)+(t_1*(x+6))/(x+6)+(9*x*(x+6))/(x+6) = 0

t_1*(x+6)+9*x*(x+6)+6 = 0

t_1*x+6*t_1+9*x^2+54*x+6 = 0

(t_1*x+6*t_1+9*x^2+54*x+6)/(x+6) = 0

(t_1*x+6*t_1+9*x^2+54*x+6)/(x+6) = 0 // * x+6

t_1*x+6*t_1+9*x^2+54*x+6 = 0

6*t_1+9*x^2+54*x+6 = 0

DELTA = 54^2-(4*9*(6*t_1+6))

DELTA = 2916-36*(6*t_1+6)

2916-36*(6*t_1+6) = 0

2916-36*(6*t_1+6) = 0

2700-216*t_1 = 0

2700-216*t_1 = 0

2700-216*t_1 = 0 // - 2700

-216*t_1 = -2700 // : -216

t_1 = -2700/(-216)

t_1 = 25/2

DELTA = 0  <=>  t_4 = 25/2

x = -54/(2*9) i t_1 = 25/2

x = -3 i t_1 = 25/2

( x = ((2916-36*(6*t_1+6))^(1/2)-54)/(2*9) or x = (-(2916-36*(6*t_1+6))^(1/2)-54)/(2*9) ) i t_1 > 25/2

( x = ((2916-36*(6*t_1+6))^(1/2)-54)/18 or x = (-((2916-36*(6*t_1+6))^(1/2)+54))/18 ) i t_1 > 25/2

t_1-25/2 > 0

t_1-25/2 > 0 // + 25/2

t_1 > 25/2

x in { -3, ((2916-36*(6*X^2+6))^(1/2)-54)/18, (-((2916-36*(6*X^2+6))^(1/2)+54))/18 }

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