(3x^2-2)^1/4=x

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Solution for (3x^2-2)^1/4=x equation: 


x in (-oo:+oo)

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

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

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

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

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

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

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

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

DELTA = (-4)^2-(-2*3*4)

DELTA = 40

DELTA > 0

x = (40^(1/2)+4)/(2*3) or x = (4-40^(1/2))/(2*3)

x = (2*10^(1/2)+4)/6 or x = (4-2*10^(1/2))/6

(x-((4-2*10^(1/2))/6))*(x-((2*10^(1/2)+4)/6)) = 0

((x-((4-2*10^(1/2))/6))*(x-((2*10^(1/2)+4)/6)))/4 = 0

((x-((4-2*10^(1/2))/6))*(x-((2*10^(1/2)+4)/6)))/4 = 0 // * 4

(x-((4-2*10^(1/2))/6))*(x-((2*10^(1/2)+4)/6)) = 0

( x-((2*10^(1/2)+4)/6) )

x-((2*10^(1/2)+4)/6) = 0 // + (2*10^(1/2)+4)/6

x = (2*10^(1/2)+4)/6

( x-((4-2*10^(1/2))/6) )

x-((4-2*10^(1/2))/6) = 0 // + (4-2*10^(1/2))/6

x = (4-2*10^(1/2))/6

x in { (2*10^(1/2)+4)/6, (4-2*10^(1/2))/6 }

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