x^2-2/3x+n=0

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Solution for x^2-2/3x+n=0 equation: 


x in (-oo:+oo)

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

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

n+x^2-2/3*x = 0

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

DELTA = 4/9-4*n

4/9-4*n = 0

4/9-4*n = 0 // - 4/9

-4*n = -4/9 // : -4

n = -4/9/(-4)

n = 1/9

DELTA = 0  <=>  t_1 = 1/9

x = 2/3/(1*2) i n = 1/9

x = 1/3 i n = 1/9

( x = ((4/9-4*n)^(1/2)+2/3)/(1*2) or x = (2/3-(4/9-4*n)^(1/2))/(1*2) ) i n > 1/9

( x = ((4/9-4*n)^(1/2)+2/3)/2 or x = (2/3-(4/9-4*n)^(1/2))/2 ) i n > 1/9

n-1/9 > 0

n-1/9 > 0 // + 1/9

n > 1/9

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

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