Y=4/3x^2-40x+307

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Solution for Y=4/3x^2-40x+307 equation: 


x in (-oo:+oo)

Y = (4/3)*x^2-(40*x)+307 // - (4/3)*x^2-(40*x)+307

Y-((4/3)*x^2)+40*x-307 = 0

Y+(-4/3)*x^2+40*x-307 = 0

Y-4/3*x^2+40*x-307 = 0

DELTA = 40^2-(-4/3*4*(Y-307))

DELTA = 16/3*(Y-307)+1600

16/3*(Y-307)+1600 = 0

16/3*(Y-307)+1600 = 0

16/3*Y-112/3 = 0

16/3*Y-112/3 = 0

16/3*Y-112/3 = 0 // + 112/3

16/3*Y = 112/3 // : 16/3

Y = 112/3/16/3

Y = 7

DELTA = 0  <=>  t_1 = 7

x = -40/(-4/3*2) i Y = 7

x = 15 i Y = 7

( x = ((16/3*(Y-307)+1600)^(1/2)-40)/(-4/3*2) or x = (-(16/3*(Y-307)+1600)^(1/2)-40)/(-4/3*2) ) i Y > 7

( x = -3/8*((16/3*(Y-307)+1600)^(1/2)-40) or x = 3/8*((16/3*(Y-307)+1600)^(1/2)+40) ) i Y > 7

Y-7 > 0

Y-7 > 0 // + 7

Y > 7

x in { 15, -3/8*((16/3*(Y-307)+1600)^(1/2)-40), 3/8*((16/3*(Y-307)+1600)^(1/2)+40) }

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