(9-2b)(12-2b)=54

Solution for (9-2b)(12-2b)=54 equation:

(9-2b)(12-2b)=54

We move all terms to the left:

(9-2b)(12-2b)-(54)=0

We add all the numbers together, and all the variables

(-2b+9)(-2b+12)-54=0

We multiply parentheses ..

(+4b^2-24b-18b+108)-54=0

We get rid of parentheses

4b^2-24b-18b+108-54=0

We add all the numbers together, and all the variables

4b^2-42b+54=0

a = 4; b = -42; c = +54;
Δ = b2-4ac
Δ = -422-4·4·54
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-30}{2*4}=\frac{12}{8}
=1+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+30}{2*4}=\frac{72}{8}
=9
$