[GnarlyOCMD]

2b^2+b=6
b^2+1/2 b=3
b^2+1/2 b+(1/2)^2=3+(1/2)^2
(b+1/2)^2 =3+1/4
b+1/2=+or- Square root 13/4 The square root is over 13 and 4
b=-1/2+or-Square root 13/2 The square root is over just 13 Not 2
b=-1+or-Square root 13/2. The square root is over just 13 Not 2.

[Jester Race]

2x^2+x - 6=0 <=> 2x^2-3x +4x-6=0 (-6*2=-12, -12's factors which add up to 1 are -3 and 4)

<=>2x(x+2)-3(x+2)=0 <=> (2x-3)(x+2)=0 =>2x-3=0 or x+2=0 <=>x = 3/2 or x=-2

You have to set the equation equal zero then factor it or use quadratic formula to solve it

Edit nevermind reread your question, you add 1/2 squared to both sides, but you need to half it first the square it.
x^2+1/2 x+(1/4)^2=3+(1/4)^2
<=>x^2+1/2x+1/16=49/16 <=> (x+1/4)^2=49/16 <=> (x+1/4) =7/4 or (x+1/4) = -7/4 <=> x=3/2 or x=-2