y=x^2/10+3x+5

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Solution for y=x^2/10+3x+5 equation: 


x in (-oo:+oo)

y = (x^2)/10+3*x+5 // - (x^2)/10+3*x+5

y-((x^2)/10)-(3*x)-5 = 0

y-((x^2)/10)-3*x-5 = 0

y-1/10*x^2-3*x-5 = 0

DELTA = (-3)^2-(-1/10*4*(y-5))

DELTA = 2/5*(y-5)+9

2/5*(y-5)+9 = 0

2/5*(y-5)+9 = 0

2/5*y+7 = 0

2/5*y+7 = 0

2/5*y+7 = 0 // - 7

2/5*y = -7 // : 2/5

y = -7/2/5

y = -35/2

DELTA = 0  <=>  t_1 = -35/2

x = 3/(-1/10*2) i y = -35/2

x = -15 i y = -35/2

( x = ((2/5*(y-5)+9)^(1/2)+3)/(-1/10*2) or x = (3-(2/5*(y-5)+9)^(1/2))/(-1/10*2) ) i y > -35/2

( x = -5*((2/5*(y-5)+9)^(1/2)+3) or x = -5*(3-(2/5*(y-5)+9)^(1/2)) ) i y > -35/2

y+35/2 > 0

y+35/2 > 0 // - 35/2

y > -35/2

x in { -15, -5*((2/5*(y-5)+9)^(1/2)+3), -5*(3-(2/5*(y-5)+9)^(1/2)) }

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