(-x2/40)+(31x/40)+(4/5)=y

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Solution for (-x2/40)+(31x/40)+(4/5)=y equation: 


x in (-oo:+oo)

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

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

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

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

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

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

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

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

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

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