(7-b)*(12-b)=24

Solution for (7-b)*(12-b)=24 equation:

(7-b)(12-b)=24

We move all terms to the left:

(7-b)(12-b)-(24)=0

We add all the numbers together, and all the variables

(-1b+7)(-1b+12)-24=0

We multiply parentheses ..

(+b^2-12b-7b+84)-24=0

We get rid of parentheses

b^2-12b-7b+84-24=0

We add all the numbers together, and all the variables

b^2-19b+60=0

a = 1; b = -19; c = +60;
Δ = b2-4ac
Δ = -192-4·1·60
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-11}{2*1}=\frac{8}{2}
=4
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+11}{2*1}=\frac{30}{2}
=15
$