Y=1/4x2-2x-5

Solution for Y=1/4x2-2x-5 equation:

x in (-oo:+oo)

Y = (1/4)*x^2-(2*x)-5 // - (1/4)*x^2-(2*x)-5

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

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

Y-1/4*x^2+2*x+5 = 0

DELTA = 2^2-(-1/4*4*(Y+5))

DELTA = Y+9

Y+9 = 0

Y+9 = 0 // - 9

Y = -9

DELTA = 0  <=>  t_1 = -9

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

x = 4 i Y = -9

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

( x = -2*((Y+9)^(1/2)-2) or x = 2*((Y+9)^(1/2)+2) ) i Y > -9

Y+9 > 0

Y+9 > 0 // - 9

Y > -9

x in { 4, -2*((Y+9)^(1/2)-2), 2*((Y+9)^(1/2)+2) }