1/2(y+4)=(x-7)^2

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Solution for 1/2(y+4)=(x-7)^2 equation: 


x in (-oo:+oo)

(1/2)*(y+4) = (x-7)^2 // - (x-7)^2

(1/2)*(y+4)-(x-7)^2 = 0

1/2*(y+4)-1*(x-7)^2 = 0

1/2*(y+4)-1*(x-7)^2 = 0

14*x-x^2+1/2*y-47 = 0

14*x-x^2+1/2*y-47 = 0

14*x-x^2+1/2*y-47 = 0

DELTA = 14^2-(-1*4*(1/2*y-47))

DELTA = 4*(1/2*y-47)+196

4*(1/2*y-47)+196 = 0

4*(1/2*y-47)+196 = 0

2*y+8 = 0

2*y+8 = 0

2*y+8 = 0 // - 8

2*y = -8 // : 2

y = -8/2

y = -4

DELTA = 0  <=>  t_3 = -4

x = -14/(-1*2) i y = -4

x = 7 i y = -4

( x = ((4*(1/2*y-47)+196)^(1/2)-14)/(-1*2) or x = (-(4*(1/2*y-47)+196)^(1/2)-14)/(-1*2) ) i y > -4

( x = ((4*(1/2*y-47)+196)^(1/2)-14)/(-2) or x = ((4*(1/2*y-47)+196)^(1/2)+14)/2 ) i y > -4

y+4 > 0

y+4 > 0 // - 4

y > -4

x in { 7, ((4*(1/2*y-47)+196)^(1/2)-14)/(-2), ((4*(1/2*y-47)+196)^(1/2)+14)/2 }

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