x^4/3+2x^2/3-24=0

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Solution for x^4/3+2x^2/3-24=0 equation: 


x in (-oo:+oo)

(x^4)/3+(2*x^2)/3-24 = 0

1/3*x^4+2/3*x^2-24 = 0

t_1 = x^2

1/3*t_1^2+2/3*t_1^1-24 = 0

1/3*t_1^2+2/3*t_1-24 = 0

DELTA = (2/3)^2-(-24*1/3*4)

DELTA = 292/9

DELTA > 0

t_1 = ((292/9)^(1/2)-2/3)/(1/3*2) or t_1 = (-(292/9)^(1/2)-2/3)/(1/3*2)

t_1 = 3/2*((292/9)^(1/2)-2/3) or t_1 = -3/2*((292/9)^(1/2)+2/3)

t_1 = -3/2*((292/9)^(1/2)+2/3)

x^2-(-3/2*((292/9)^(1/2)+2/3)) = 0

x^2+3/2*((292/9)^(1/2)+2/3) = 0

1*x^2 = -(3/2*((292/9)^(1/2)+2/3)) // : 1

x^2 = -3/2*((292/9)^(1/2)+2/3)

t_1 = 3/2*((292/9)^(1/2)-2/3)

x^2-(3/2*((292/9)^(1/2)-2/3)) = 0

x^2-3/2*((292/9)^(1/2)-2/3) = 0

1*x^2 = -(-3/2*((292/9)^(1/2)-2/3)) // : 1

x^2 = 3/2*((292/9)^(1/2)-2/3)

x^2 = 3/2*((292/9)^(1/2)-2/3) // ^ 1/2

abs(x) = (3/2)^(1/2)*((292/9)^(1/2)-2/3)^(1/2)

x = (3/2)^(1/2)*((292/9)^(1/2)-2/3)^(1/2) or x = -((3/2)^(1/2)*((292/9)^(1/2)-2/3)^(1/2))

x in { (3/2)^(1/2)*((292/9)^(1/2)-2/3)^(1/2), -((3/2)^(1/2)*((292/9)^(1/2)-2/3)^(1/2)) }

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