x^4/3-x^2/3-8=0

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Solution for x^4/3-x^2/3-8=0 equation: 


x in (-oo:+oo)

(x^4)/3-((x^2)/3)-8 = 0

1/3*x^4-1/3*x^2-8 = 0

t_1 = x^2

1/3*t_1^2-1/3*t_1^1-8 = 0

1/3*t_1^2-1/3*t_1-8 = 0

DELTA = (-1/3)^2-(-8*1/3*4)

DELTA = 97/9

DELTA > 0

t_1 = ((97/9)^(1/2)+1/3)/(1/3*2) or t_1 = (1/3-(97/9)^(1/2))/(1/3*2)

t_1 = 3/2*((97/9)^(1/2)+1/3) or t_1 = 3/2*(1/3-(97/9)^(1/2))

t_1 = 3/2*(1/3-(97/9)^(1/2))

x^2-(3/2*(1/3-(97/9)^(1/2))) = 0

x^2-3/2*(1/3-(97/9)^(1/2)) = 0

1*x^2 = -(-3/2*(1/3-(97/9)^(1/2))) // : 1

x^2 = 3/2*(1/3-(97/9)^(1/2))

t_1 = 3/2*((97/9)^(1/2)+1/3)

x^2-(3/2*((97/9)^(1/2)+1/3)) = 0

x^2-3/2*((97/9)^(1/2)+1/3) = 0

1*x^2 = -(-3/2*((97/9)^(1/2)+1/3)) // : 1

x^2 = 3/2*((97/9)^(1/2)+1/3)

x^2 = 3/2*((97/9)^(1/2)+1/3) // ^ 1/2

abs(x) = (3/2)^(1/2)*((97/9)^(1/2)+1/3)^(1/2)

x = (3/2)^(1/2)*((97/9)^(1/2)+1/3)^(1/2) or x = -((3/2)^(1/2)*((97/9)^(1/2)+1/3)^(1/2))

x in { (3/2)^(1/2)*((97/9)^(1/2)+1/3)^(1/2), -((3/2)^(1/2)*((97/9)^(1/2)+1/3)^(1/2)) }

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