4b(3b-1)=9-b

Solution for 4b(3b-1)=9-b equation:

4b(3b-1)=9-b

We move all terms to the left:

4b(3b-1)-(9-b)=0

We add all the numbers together, and all the variables

4b(3b-1)-(-1b+9)=0

We multiply parentheses

12b^2-4b-(-1b+9)=0

We get rid of parentheses

12b^2-4b+1b-9=0

We add all the numbers together, and all the variables

12b^2-3b-9=0

a = 12; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·12·(-9)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*12}=\frac{-18}{24}
=-3/4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*12}=\frac{24}{24}
=1
$