Y=1/3(x-6)(x-1)

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Solution for Y=1/3(x-6)(x-1) equation: 


x in (-oo:+oo)

Y = (1/3)*(x-6)*(x-1) // - (1/3)*(x-6)*(x-1)

Y-((1/3)*(x-6)*(x-1)) = 0

(-1/3)*(x-1)*(x-6)+Y = 0

Y-1/3*(x-1)*(x-6) = 0

Y-1/3*(x-1)*(x-6) = 0

Y-1/3*x^2+7/3*x-2 = 0

Y-1/3*x^2+7/3*x-2 = 0

Y-1/3*x^2+7/3*x-2 = 0

DELTA = (7/3)^2-(-1/3*4*(Y-2))

DELTA = 4/3*(Y-2)+49/9

4/3*(Y-2)+49/9 = 0

(4/3*9*(Y-2))/9+49/9 = 0

4/3*9*(Y-2)+49 = 0

12*Y+25 = 0

(12*Y+25)/9 = 0

(12*Y+25)/9 = 0 // * 9

12*Y+25 = 0

12*Y+25 = 0 // - 25

12*Y = -25 // : 12

Y = -25/12

DELTA = 0  <=>  t_3 = -25/12

x = -7/3/(-1/3*2) i Y = -25/12

x = 7/2 i Y = -25/12

( x = ((4/3*(Y-2)+49/9)^(1/2)-7/3)/(-1/3*2) or x = (-(4/3*(Y-2)+49/9)^(1/2)-7/3)/(-1/3*2) ) i Y > -25/12

( x = -3/2*((4/3*(Y-2)+49/9)^(1/2)-7/3) or x = 3/2*((4/3*(Y-2)+49/9)^(1/2)+7/3) ) i Y > -25/12

Y-(-25/12) > 0

Y+25/12 > 0

Y+25/12 > 0 // - 25/12

Y > -25/12

x in { 7/2, -3/2*((4/3*(Y-2)+49/9)^(1/2)-7/3), 3/2*((4/3*(Y-2)+49/9)^(1/2)+7/3) }

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