(-1/3*e^(-x^2/6)*x)*(9x^2-x^4/3)

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Solution for (-1/3*e^(-x^2/6)*x)*(9x^2-x^4/3) equation: 


x in (-oo:+oo)

(-1/3)*x*e^(((-x)^2)/6)*(9*x^2-((x^4)/3)) = 0

(-1/3)*x*e^(((-x)^2)/6) = 0

(-1/3)*x = 0

-1/3*x = 0 // : -1/3

x = 0

e^(((-x)^2)/6) = 0

x należy do O

(-1/3)*x*e^(((-x)^2)/6) = 0  <=>  (-1/3)*x = 0 or (-1/3)*x*e^(((-x)^2)/6) = 0  <=>  e^(((-x)^2)/6) = 0

9*x^2-((x^4)/3) = 0

9*x^2-1/3*x^4 = 0

t_1 = x^2

9*t_1^1-1/3*t_1^2 = 0

9*t_1-1/3*t_1^2 = 0

DELTA = 9^2-(-1/3*0*4)

DELTA = 81

DELTA > 0

t_1 = (81^(1/2)-9)/(-1/3*2) or t_1 = (-81^(1/2)-9)/(-1/3*2)

t_1 = 0 or t_1 = 27

t_1 = 0

x^2+0 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

t_1 = 27

x^2-27 = 0

1*x^2 = 27 // : 1

x^2 = 27

x^2 = 27 // ^ 1/2

abs(x) = 3*3^(1/2)

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

(-1/3)*x*e^(((-x)^2)/6)*(9*x^2-((x^4)/3)) = 0  <=>  (-1/3)*x*e^(((-x)^2)/6) = 0 or (-1/3)*x*e^(((-x)^2)/6)*(9*x^2-((x^4)/3)) = 0  <=>  9*x^2-((x^4)/3) = 0

x in { 0, 0, 3*3^(1/2), -(3*3^(1/2)) }

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