(x-2/3)(x^4-13/6x^2+1)=0

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Solution for (x-2/3)(x^4-13/6x^2+1)=0 equation: 


x in (-oo:+oo)

(x-(2/3))*(x^4-((13/6)*x^2)+1) = 0

(x-2/3)*(x^4+(-13/6)*x^2+1) = 0

(x-2/3)*(x^4-13/6*x^2+1) = 0

( x-2/3 )

x-2/3 = 0 // + 2/3

x = 2/3

x-(2/3) = 0

x-2/3 = 0

x-2/3 = 0 // + 2/3

x = 2/3

x^4-((13/6)*x^2)+1 = 0

x^4+(-13/6)*x^2+1 = 0

x^4-13/6*x^2+1 = 0

t_1 = x^2

1*t_1^2-13/6*t_1^1+1 = 0

t_1^2-13/6*t_1+1 = 0

DELTA = (-13/6)^2-(1*1*4)

DELTA = 25/36

DELTA > 0

t_1 = ((25/36)^(1/2)+13/6)/(1*2) or t_1 = (13/6-(25/36)^(1/2))/(1*2)

t_1 = 3/2 or t_1 = 2/3

t_1 = 2/3

x^2-2/3 = 0

1*x^2 = 2/3 // : 1

x^2 = 2/3

x^2 = 2/3 // ^ 1/2

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

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

t_1 = 3/2

x^2-3/2 = 0

1*x^2 = 3/2 // : 1

x^2 = 3/2

x^2 = 3/2 // ^ 1/2

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

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

(x-(2/3))*(x^4-((13/6)*x^2)+1) = 0  <=>  x-(2/3) = 0 or (x-(2/3))*(x^4-((13/6)*x^2)+1) = 0  <=>  x^4-((13/6)*x^2)+1 = 0

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

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