y=x^2/2+3x

Solution for y=x^2/2+3x equation:

x in (-oo:+oo)

y = (x^2)/2+3*x // - (x^2)/2+3*x

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

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

y-1/2*x^2-3*x = 0

DELTA = (-3)^2-(-1/2*4*y)

DELTA = 2*y+9

2*y+9 = 0

2*y+9 = 0 // - 9

2*y = -9 // : 2

y = -9/2

DELTA = 0  <=>  t_1 = -9/2

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

x = -3 i y = -9/2

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

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

y-(-9/2) > 0

y+9/2 > 0

y+9/2 > 0 // - 9/2

y > -9/2

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