5y+4=(x+3)^2+1/2

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Solution for 5y+4=(x+3)^2+1/2 equation: 


x in (-oo:+oo)

5*y+4 = (x+3)^2+1/2 // - (x+3)^2+1/2

5*y-(x+3)^2-(1/2)+4 = 0

5*y-(x+3)^2-1/2+4 = 0

5*y-1*(x+3)^2-1/2+4 = 0

(-1*2*(x+3)^2)/2+(2*5*y)/2-1/2+(2*4)/2 = 0

2*5*y-1*2*(x+3)^2+2*4-1 = 0

10*y-2*x^2-12*x-18-1+8 = 0

10*y-2*x^2-12*x-19+8 = 0

10*y-2*x^2-12*x-11 = 0

(10*y-2*x^2-12*x-11)/2 = 0

(10*y-2*x^2-12*x-11)/2 = 0 // * 2

10*y-2*x^2-12*x-11 = 0

10*y-2*x^2-12*x-11 = 0

DELTA = (-12)^2-(-2*4*(10*y-11))

DELTA = 8*(10*y-11)+144

8*(10*y-11)+144 = 0

8*(10*y-11)+144 = 0

80*y+56 = 0

80*y+56 = 0

80*y+56 = 0 // - 56

80*y = -56 // : 80

y = -56/80

y = -7/10

DELTA = 0  <=>  t_3 = -7/10

x = 12/(-2*2) i y = -7/10

x = -3 i y = -7/10

( x = ((8*(10*y-11)+144)^(1/2)+12)/(-2*2) or x = (12-(8*(10*y-11)+144)^(1/2))/(-2*2) ) i y > -7/10

( x = ((8*(10*y-11)+144)^(1/2)+12)/(-4) or x = (12-(8*(10*y-11)+144)^(1/2))/(-4) ) i y > -7/10

y+7/10 > 0

y+7/10 > 0 // - 7/10

y > -7/10

x in { -3, ((8*(10*y-11)+144)^(1/2)+12)/(-4), (12-(8*(10*y-11)+144)^(1/2))/(-4) }

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