(2x^2-7)^1/2=x

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Solution for (2x^2-7)^1/2=x equation: 


x in (-oo:+oo)

((2*x^2-7)^1)/2 = x // - x

((2*x^2-7)^1)/2-x = 0

(2*x^2-7)/2-x = 0

(2*x^2-7)/2+(2*(-x))/2 = 0

2*x^2+2*(-x)-7 = 0

2*x^2-2*x-7 = 0

2*x^2-2*x-7 = 0

2*x^2-2*x-7 = 0

DELTA = (-2)^2-(-7*2*4)

DELTA = 60

DELTA > 0

x = (60^(1/2)+2)/(2*2) or x = (2-60^(1/2))/(2*2)

x = (2*15^(1/2)+2)/4 or x = (2-2*15^(1/2))/4

(x-((2-2*15^(1/2))/4))*(x-((2*15^(1/2)+2)/4)) = 0

((x-((2-2*15^(1/2))/4))*(x-((2*15^(1/2)+2)/4)))/2 = 0

((x-((2-2*15^(1/2))/4))*(x-((2*15^(1/2)+2)/4)))/2 = 0 // * 2

(x-((2-2*15^(1/2))/4))*(x-((2*15^(1/2)+2)/4)) = 0

( x-((2*15^(1/2)+2)/4) )

x-((2*15^(1/2)+2)/4) = 0 // + (2*15^(1/2)+2)/4

x = (2*15^(1/2)+2)/4

( x-((2-2*15^(1/2))/4) )

x-((2-2*15^(1/2))/4) = 0 // + (2-2*15^(1/2))/4

x = (2-2*15^(1/2))/4

x in { (2*15^(1/2)+2)/4, (2-2*15^(1/2))/4 }

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