(10x^2-24)^1/4=x

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Solution for (10x^2-24)^1/4=x equation: 


x in (-oo:+oo)

((10*x^2-24)^1)/4 = x // - x

((10*x^2-24)^1)/4-x = 0

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

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

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

10*x^2-4*x-24 = 0

10*x^2-4*x-24 = 0

2*(5*x^2-2*x-12) = 0

5*x^2-2*x-12 = 0

DELTA = (-2)^2-(-12*4*5)

DELTA = 244

DELTA > 0

x = (244^(1/2)+2)/(2*5) or x = (2-244^(1/2))/(2*5)

x = (2*61^(1/2)+2)/10 or x = (2-2*61^(1/2))/10

2*(x-((2-2*61^(1/2))/10))*(x-((2*61^(1/2)+2)/10)) = 0

(2*(x-((2-2*61^(1/2))/10))*(x-((2*61^(1/2)+2)/10)))/4 = 0

(2*(x-((2-2*61^(1/2))/10))*(x-((2*61^(1/2)+2)/10)))/4 = 0 // * 4

2*(x-((2-2*61^(1/2))/10))*(x-((2*61^(1/2)+2)/10)) = 0

( x-((2*61^(1/2)+2)/10) )

x-((2*61^(1/2)+2)/10) = 0 // + (2*61^(1/2)+2)/10

x = (2*61^(1/2)+2)/10

( x-((2-2*61^(1/2))/10) )

x-((2-2*61^(1/2))/10) = 0 // + (2-2*61^(1/2))/10

x = (2-2*61^(1/2))/10

x in { (2*61^(1/2)+2)/10, (2-2*61^(1/2))/10 }

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