12=2b^2-2b+1

Solution for 12=2b^2-2b+1 equation:

12=2b^2-2b+1

We move all terms to the left:

12-(2b^2-2b+1)=0

We get rid of parentheses

-2b^2+2b-1+12=0

We add all the numbers together, and all the variables

-2b^2+2b+11=0

a = -2; b = 2; c = +11;
Δ = b2-4ac
Δ = 22-4·(-2)·11
Δ = 92
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{23}}{2*-2}=\frac{-2-2\sqrt{23}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{23}}{2*-2}=\frac{-2+2\sqrt{23}}{-4}
$