(p+1/2)^2=9/4

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Solution for (p+1/2)^2=9/4 equation: 


p in (-oo:+oo)

(p+1/2)^2 = 9/4 // - 9/4

(p+1/2)^2-(9/4) = 0

(p+1/2)^2-9/4 = 0

(4*(p+1/2)^2)/4-9/4 = 0

4*(p+1/2)^2-9 = 0

4*p^2+4*p-8 = 0

4*p^2+4*p-8 = 0

4*(p^2+p-2) = 0

p^2+p-2 = 0

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

DELTA = 9

DELTA > 0

p = (9^(1/2)-1)/(1*2) or p = (-9^(1/2)-1)/(1*2)

p = 1 or p = -2

4*(p+2)*(p-1) = 0

(4*(p+2)*(p-1))/4 = 0

(4*(p+2)*(p-1))/4 = 0 // * 4

4*(p+2)*(p-1) = 0

( p+2 )

p+2 = 0 // - 2

p = -2

( p-1 )

p-1 = 0 // + 1

p = 1

p in { -2, 1 }

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