y=x^2-5/3x-20

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Solution for y=x^2-5/3x-20 equation: 


x in (-oo:+oo)

y = x^2-((5/3)*x)-20 // - x^2-((5/3)*x)-20

(5/3)*x-x^2+y+20 = 0

5/3*x-x^2+y+20 = 0

DELTA = (5/3)^2-(-1*4*(y+20))

DELTA = 4*(y+20)+25/9

4*(y+20)+25/9 = 0

(4*9*(y+20))/9+25/9 = 0

4*9*(y+20)+25 = 0

36*y+745 = 0

(36*y+745)/9 = 0

(36*y+745)/9 = 0 // * 9

36*y+745 = 0

36*y+745 = 0 // - 745

36*y = -745 // : 36

y = -745/36

DELTA = 0  <=>  t_1 = -745/36

x = -5/3/(-1*2) i y = -745/36

x = 5/6 i y = -745/36

( x = ((4*(y+20)+25/9)^(1/2)-5/3)/(-1*2) or x = (-(4*(y+20)+25/9)^(1/2)-5/3)/(-1*2) ) i y > -745/36

( x = ((4*(y+20)+25/9)^(1/2)-5/3)/(-2) or x = ((4*(y+20)+25/9)^(1/2)+5/3)/2 ) i y > -745/36

y-(-745/36) > 0

y+745/36 > 0

y+745/36 > 0 // - 745/36

y > -745/36

x in { 5/6, ((4*(y+20)+25/9)^(1/2)-5/3)/(-2), ((4*(y+20)+25/9)^(1/2)+5/3)/2 }

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