3/2(n+1)^2=33

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Solution for 3/2(n+1)^2=33 equation: 


n in (-oo:+oo)

(3/2)*(n+1)^2 = 33 // - 33

(3/2)*(n+1)^2-33 = 0

3/2*(n+1)^2-33 = 0

3/2*(n+1)^2-33 = 0

3/2*n^2+3*n-63/2 = 0

3/2*n^2+3*n-63/2 = 0

3*(1/2*n^2+n-21/2) = 0

1/2*n^2+n-21/2 = 0

DELTA = 1^2-(-21/2*1/2*4)

DELTA = 22

DELTA > 0

n = (22^(1/2)-1)/(1/2*2) or n = (-22^(1/2)-1)/(1/2*2)

n = 22^(1/2)-1 or n = -(22^(1/2)+1)

3*(n+22^(1/2)+1)*(n-22^(1/2)+1) = 0

3*(n+22^(1/2)+1)*(n-22^(1/2)+1) = 0

( n+22^(1/2)+1 )

n+22^(1/2)+1 = 0 // - 22^(1/2)+1

n = -(22^(1/2)+1)

( n-22^(1/2)+1 )

n-22^(1/2)+1 = 0 // - 1-22^(1/2)

n = -(1-22^(1/2))

n = 22^(1/2)-1

n in { -(22^(1/2)+1), 22^(1/2)-1 }

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