(x+12)(x+9)=180

Solution for (x+12)(x+9)=180 equation:

(x+12)(x+9)=180

We move all terms to the left:

(x+12)(x+9)-(180)=0

We multiply parentheses ..

(+x^2+9x+12x+108)-180=0

We get rid of parentheses

x^2+9x+12x+108-180=0

We add all the numbers together, and all the variables

x^2+21x-72=0

a = 1; b = 21; c = -72;
Δ = b2-4ac
Δ = 212-4·1·(-72)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*1}=\frac{6}{2}
=3
$