y=x^4/2-x^2-8

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Solution for y=x^4/2-x^2-8 equation: 


x in (-oo:+oo)

y = (x^4)/2-x^2-8 // - (x^4)/2-x^2-8

x^2-((x^4)/2)+y+8 = 0

x^2-1/2*x^4+y+8 = 0

t_1 = x^2

1*t_1^1-1/2*t_1^2+y+8 = 0

t_1-1/2*t_1^2+y+8 = 0

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

DELTA = 2*(y+8)+1

2*(y+8)+1 = 0

2*(y+8)+1 = 0

2*y+17 = 0

2*y+17 = 0

2*y+17 = 0 // - 17

2*y = -17 // : 2

y = -17/2

DELTA = 0  <=>  t_2 = -17/2

t_1 = -1/(-1/2*2) i y = -17/2

t_1 = 1 i y = -17/2

( t_1 = ((2*(y+8)+1)^(1/2)-1)/(-1/2*2) or t_1 = (-(2*(y+8)+1)^(1/2)-1)/(-1/2*2) ) i y > -17/2

( t_1 = 1-(2*(y+8)+1)^(1/2) or t_1 = (2*(y+8)+1)^(1/2)+1 ) i y > -17/2

y-(-17/2) > 0

y+17/2 > 0

y+17/2 > 0 // - 17/2

y > -17/2

t_1 = 1

x^2-1 = 0

1*x^2 = 1 // : 1

x^2 = 1

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

t_1 = 1-(2*(y+8)+1)^(1/2)

t_3 = (2*(y+8)+1)^(1/2)-1

t_3+x^2 = 0

1*x^2 = -t_3 // : 1

x^2 = -t_3

x^2 = -t_3 // ^ 1/2

abs(x) = (-t_3)^(1/2)

x = (-t_3)^(1/2) or x = -(-t_3)^(1/2)

t_1 = (2*(y+8)+1)^(1/2)+1

t_4 = -(2*(y+8)+1)^(1/2)-1

t_4+x^2 = 0

1*x^2 = -t_4 // : 1

x^2 = -t_4

x^2 = -t_4 // ^ 1/2

abs(x) = (-t_4)^(1/2)

x = (-t_4)^(1/2) or x = -(-t_4)^(1/2)

x in { 1, -1, (-((2*(y+8)+1)^(1/2)-1))^(1/2), -(-((2*(y+8)+1)^(1/2)-1))^(1/2), (-(-(2*(y+8)+1)^(1/2)-1))^(1/2), -(-(-(2*(y+8)+1)^(1/2)-1))^(1/2) }

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