12y-6x^2/3y^2-12x

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Solution for 12y-6x^2/3y^2-12x equation: 


x in (-oo:+oo)

12*y-(12*x)-(((6*x^2)/3)*y^2) = 0

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

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

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

DELTA = 96*y^3+144

96*y^3+144 = 0

96*y^3 = -144 // : 96

y^3 = -3/2

y^3 = -3/2 // ^ 1/3

y = -(3/2)^(1/3)

DELTA = 0  <=>  t_1 = -(3/2)^(1/3)

x = 12/(-2*2*y^2) i y = -(3/2)^(1/3)

x = -3*y^-2 i y = -(3/2)^(1/3)

( x = ((96*y^3+144)^(1/2)+12)/(-2*2*y^2) or x = (12-(96*y^3+144)^(1/2))/(-2*2*y^2) ) i y > -(3/2)^(1/3)

( x = ((96*y^3+144)^(1/2)+12)/(-4*y^2) or x = (12-(96*y^3+144)^(1/2))/(-4*y^2) ) i y > -(3/2)^(1/3)

y+(3/2)^(1/3) > 0

y+(3/2)^(1/3) > 0 // - (3/2)^(1/3)

y > -(3/2)^(1/3)

x in { -3*y^-2, ((96*y^3+144)^(1/2)+12)/(-4*y^2), (12-(96*y^3+144)^(1/2))/(-4*y^2) }

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