(n-5)=x^2-6/2x

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Solution for (n-5)=x^2-6/2x equation: 


x in (-oo:+oo)

n-5 = x^2-((6/2)*x) // - x^2-((6/2)*x)

n-x^2+(6/2)*x-5 = 0

n-x^2+3*x-5 = 0

DELTA = 3^2-(-1*4*(n-5))

DELTA = 4*(n-5)+9

4*(n-5)+9 = 0

4*(n-5)+9 = 0

4*n-11 = 0

4*n-11 = 0

4*n-11 = 0 // + 11

4*n = 11 // : 4

n = 11/4

DELTA = 0  <=>  t_1 = 11/4

x = -3/(-1*2) i n = 11/4

x = 3/2 i n = 11/4

( x = ((4*(n-5)+9)^(1/2)-3)/(-1*2) or x = (-(4*(n-5)+9)^(1/2)-3)/(-1*2) ) i n > 11/4

( x = ((4*(n-5)+9)^(1/2)-3)/(-2) or x = ((4*(n-5)+9)^(1/2)+3)/2 ) i n > 11/4

n-(11/4) > 0

n-11/4 > 0

n-11/4 > 0 // + 11/4

n > 11/4

x in { 3/2, ((4*(n-5)+9)^(1/2)-3)/(-2), ((4*(n-5)+9)^(1/2)+3)/2 }

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