y=1/4x^2+1/2x+9/4

Solution for y=1/4x^2+1/2x+9/4 equation:

x in (-oo:+oo)

y = (1/4)*x^2+(1/2)*x+9/4 // - (1/4)*x^2+(1/2)*x+9/4

y-((1/4)*x^2)-((1/2)*x)-(9/4) = 0

(-1/4)*x^2+(-1/2)*x+y-9/4 = 0

y-1/4*x^2-1/2*x-9/4 = 0

DELTA = (-1/2)^2-(-1/4*4*(y-9/4))

DELTA = y-2

y-2 = 0

y-2 = 0 // + 2

y = 2

DELTA = 0  <=>  t_1 = 2

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

x = -1 i y = 2

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

( x = -2*((y-2)^(1/2)+1/2) or x = -2*(1/2-(y-2)^(1/2)) ) i y > 2

y-2 > 0

y-2 > 0 // + 2

y > 2

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