Y=2/3x^2-3x-54

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Solution for Y=2/3x^2-3x-54 equation: 


x in (-oo:+oo)

Y = (2/3)*x^2-(3*x)-54 // - (2/3)*x^2-(3*x)-54

Y-((2/3)*x^2)+3*x+54 = 0

Y+(-2/3)*x^2+3*x+54 = 0

Y-2/3*x^2+3*x+54 = 0

DELTA = 3^2-(-2/3*4*(Y+54))

DELTA = 8/3*(Y+54)+9

8/3*(Y+54)+9 = 0

8/3*(Y+54)+9 = 0

8/3*Y+153 = 0

8/3*Y+153 = 0

8/3*Y+153 = 0 // - 153

8/3*Y = -153 // : 8/3

Y = -153/8/3

Y = -459/8

DELTA = 0  <=>  t_1 = -459/8

x = -3/(-2/3*2) i Y = -459/8

x = 9/4 i Y = -459/8

( x = ((8/3*(Y+54)+9)^(1/2)-3)/(-2/3*2) or x = (-(8/3*(Y+54)+9)^(1/2)-3)/(-2/3*2) ) i Y > -459/8

( x = -3/4*((8/3*(Y+54)+9)^(1/2)-3) or x = 3/4*((8/3*(Y+54)+9)^(1/2)+3) ) i Y > -459/8

Y+459/8 > 0

Y+459/8 > 0 // - 459/8

Y > -459/8

x in { 9/4, -3/4*((8/3*(Y+54)+9)^(1/2)-3), 3/4*((8/3*(Y+54)+9)^(1/2)+3) }

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