3b(b-1)=2b+2

Solution for 3b(b-1)=2b+2 equation:

3b(b-1)=2b+2

We move all terms to the left:

3b(b-1)-(2b+2)=0

We multiply parentheses

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

We get rid of parentheses

3b^2-3b-2b-2=0

We add all the numbers together, and all the variables

3b^2-5b-2=0

a = 3; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·3·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*3}=\frac{-2}{6}
=-1/3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*3}=\frac{12}{6}
=2
$