-1=(x^2+3x)/(3x+9)-p^2

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Solution for -1=(x^2+3x)/(3x+9)-p^2 equation: 


D( x )

3*x+9 = 0

3*x+9 = 0

3*x+9 = 0

3*x+9 = 0 // - 9

3*x = -9 // : 3

x = -9/3

x = -3

x in (-oo:-3) U (-3:+oo)

-1 = (x^2+3*x)/(3*x+9)-p^2 // - (x^2+3*x)/(3*x+9)-p^2

p^2-((x^2+3*x)/(3*x+9))-1 = 0

(-1*(x^2+3*x))/(3*x+9)+p^2-1 = 0

(-1*(x^2+3*x))/(3*x+9)+(p^2*(3*x+9))/(3*x+9)+(-1*(3*x+9))/(3*x+9) = 0

p^2*(3*x+9)-1*(x^2+3*x)-1*(3*x+9) = 0

3*p^2*x+9*p^2-x^2-3*x-3*x-9 = 0

3*p^2*x+9*p^2-x^2-6*x-9 = 0

(3*p^2*x+9*p^2-x^2-6*x-9)/(3*x+9) = 0

(3*p^2*x+9*p^2-x^2-6*x-9)/(3*x+9) = 0 // * 3*x+9

3*p^2*x+9*p^2-x^2-6*x-9 = 0

9*p^2-x^2-6*x-9 = 0

DELTA = (-6)^2-(-1*4*(9*p^2-9))

DELTA = 4*(9*p^2-9)+36

4*(9*p^2-9)+36 = 0

4*(9*p^2-9)+36 = 0

36*p^2 = 0

36*p^2 = 0

36*p^2 = 0 // : 36

p^2 = 0

p = 0

DELTA = 0  <=>  t_3 = 0

x = 6/(-1*2) i p = 0

x = -3 i p = 0

( x = ((4*(9*p^2-9)+36)^(1/2)+6)/(-1*2) or x = (6-(4*(9*p^2-9)+36)^(1/2))/(-1*2) ) i p > 0

( x = ((4*(9*p^2-9)+36)^(1/2)+6)/(-2) or x = (6-(4*(9*p^2-9)+36)^(1/2))/(-2) ) i p > 0

p+0 > 0

p > 0

p+0 > 0 // - 0

p > 0

x in { -3 i p -> {0}} 

x in { ((4*(9*p^2-9)+36)^(1/2)+6)/(-2), (6-(4*(9*p^2-9)+36)^(1/2))/(-2) }

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