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

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Solution for x^2-(1/3x)*x^3 equation:


x in (-oo:+oo)

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

(-1/3)*x^4+x^2 = 0

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

t_1 = x^2

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

t_1-1/3*t_1^2 = 0

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

DELTA = 1

DELTA > 0

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

t_1 = 0 or t_1 = 3

t_1 = 0

x^2+0 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

t_1 = 3

x^2-3 = 0

1*x^2 = 3 // : 1

x^2 = 3

x^2 = 3 // ^ 1/2

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

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

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

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