X^1/2+8x=x^2-6

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Solution for X^1/2+8x=x^2-6 equation: 


x in (-oo:+oo)

(X^1)/2+8*x = x^2-6 // - x^2-6

(X^1)/2-x^2+8*x+6 = 0

X/2-x^2+8*x+6 = 0

1/2*X-x^2+8*x+6 = 0

DELTA = 8^2-(-1*4*(1/2*X+6))

DELTA = 4*(1/2*X+6)+64

4*(1/2*X+6)+64 = 0

4*(1/2*X+6)+64 = 0

2*X+88 = 0

2*X+88 = 0

2*X+88 = 0 // - 88

2*X = -88 // : 2

X = -88/2

X = -44

DELTA = 0  <=>  t_1 = -44

x = -8/(-1*2) i X = -44

x = 4 i X = -44

( x = ((4*(1/2*X+6)+64)^(1/2)-8)/(-1*2) or x = (-(4*(1/2*X+6)+64)^(1/2)-8)/(-1*2) ) i X > -44

( x = ((4*(1/2*X+6)+64)^(1/2)-8)/(-2) or x = ((4*(1/2*X+6)+64)^(1/2)+8)/2 ) i X > -44

X+44 > 0

X+44 > 0 // - 44

X > -44

x in { 4, ((4*(1/2*X+6)+64)^(1/2)-8)/(-2), ((4*(1/2*X+6)+64)^(1/2)+8)/2 }

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