x^2+4y^2+3x-8y=55/4

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Solution for x^2+4y^2+3x-8y=55/4 equation: 


x in (-oo:+oo)

t_1 = 4*y^2-8*y-55/4

t_1+x^2+3*x = 0

t_1+x^2+3*x = 0

DELTA = 3^2-(1*4*t_1)

DELTA = 9-4*t_1

9-4*t_1 = 0

9-4*t_1 = 0 // - 9

-4*t_1 = -9 // : -4

t_1 = -9/(-4)

t_1 = 9/4

DELTA = 0  <=>  t_2 = 9/4

x = -3/(1*2) i t_1 = 9/4

x = -3/2 i t_1 = 9/4

( x = ((9-4*t_1)^(1/2)-3)/(1*2) or x = (-(9-4*t_1)^(1/2)-3)/(1*2) ) i t_1 > 9/4

( x = ((9-4*t_1)^(1/2)-3)/2 or x = (-((9-4*t_1)^(1/2)+3))/2 ) i t_1 > 9/4

t_1-9/4 > 0

t_1-9/4 > 0 // + 9/4

t_1 > 9/4

x in { -3/2, ((9-4*(4*y^2-8*y-55/4))^(1/2)-3)/2, (-((9-4*(4*y^2-8*y-55/4))^(1/2)+3))/2 }

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