Y=1/2x^2+8x-20

Solution for Y=1/2x^2+8x-20 equation:

x in (-oo:+oo)

Y = (1/2)*x^2+8*x-20 // - (1/2)*x^2+8*x-20

Y-((1/2)*x^2)-(8*x)+20 = 0

Y+(-1/2)*x^2-8*x+20 = 0

Y-1/2*x^2-8*x+20 = 0

DELTA = (-8)^2-(-1/2*4*(Y+20))

DELTA = 2*(Y+20)+64

2*(Y+20)+64 = 0

2*(Y+20)+64 = 0

2*Y+104 = 0

2*Y+104 = 0

2*Y+104 = 0 // - 104

2*Y = -104 // : 2

Y = -104/2

Y = -52

DELTA = 0  <=>  t_1 = -52

x = 8/(-1/2*2) i Y = -52

x = -8 i Y = -52

( x = ((2*(Y+20)+64)^(1/2)+8)/(-1/2*2) or x = (8-(2*(Y+20)+64)^(1/2))/(-1/2*2) ) i Y > -52

( x = -((2*(Y+20)+64)^(1/2)+8) or x = (2*(Y+20)+64)^(1/2)-8 ) i Y > -52

Y+52 > 0

Y+52 > 0 // - 52

Y > -52

x in { -8, -((2*(Y+20)+64)^(1/2)+8), (2*(Y+20)+64)^(1/2)-8 }