y=x^2/40+31x/40+4/5

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Solution for y=x^2/40+31x/40+4/5 equation: 


x in (-oo:+oo)

y = (x^2)/40+(31*x)/40+4/5 // - (x^2)/40+(31*x)/40+4/5

y-((x^2)/40)-((31*x)/40)-(4/5) = 0

(-31/40)*x-((x^2)/40)+y-4/5 = 0

y-1/40*x^2-31/40*x-4/5 = 0

DELTA = (-31/40)^2-(-1/40*4*(y-4/5))

DELTA = 1/10*(y-4/5)+961/1600

1/10*(y-4/5)+961/1600 = 0

(1/10*1600*(y-4/5))/1600+961/1600 = 0

1/10*1600*(y-4/5)+961 = 0

160*y+833 = 0

(160*y+833)/1600 = 0

(160*y+833)/1600 = 0 // * 1600

160*y+833 = 0

160*y+833 = 0 // - 833

160*y = -833 // : 160

y = -833/160

DELTA = 0  <=>  t_1 = -833/160

x = 31/40/(-1/40*2) i y = -833/160

x = -31/2 i y = -833/160

( x = ((1/10*(y-4/5)+961/1600)^(1/2)+31/40)/(-1/40*2) or x = (31/40-(1/10*(y-4/5)+961/1600)^(1/2))/(-1/40*2) ) i y > -833/160

( x = -20*((1/10*(y-4/5)+961/1600)^(1/2)+31/40) or x = -20*(31/40-(1/10*(y-4/5)+961/1600)^(1/2)) ) i y > -833/160

y-(-833/160) > 0

y+833/160 > 0

y+833/160 > 0 // - 833/160

y > -833/160

x in { -31/2, -20*((1/10*(y-4/5)+961/1600)^(1/2)+31/40), -20*(31/40-(1/10*(y-4/5)+961/1600)^(1/2)) }

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