3-2b(b-2)=2-7b

Solution for 3-2b(b-2)=2-7b equation:

3-2b(b-2)=2-7b

We move all terms to the left:

3-2b(b-2)-(2-7b)=0

We add all the numbers together, and all the variables

-2b(b-2)-(-7b+2)+3=0

We multiply parentheses

-2b^2+4b-(-7b+2)+3=0

We get rid of parentheses

-2b^2+4b+7b-2+3=0

We add all the numbers together, and all the variables

-2b^2+11b+1=0

a = -2; b = 11; c = +1;
Δ = b2-4ac
Δ = 112-4·(-2)·1
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{129}}{2*-2}=\frac{-11-\sqrt{129}}{-4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{129}}{2*-2}=\frac{-11+\sqrt{129}}{-4}
$