(x+6)(x+9)=108

Solution for (x+6)(x+9)=108 equation:

(x+6)(x+9)=108

We move all terms to the left:

(x+6)(x+9)-(108)=0

We multiply parentheses ..

(+x^2+9x+6x+54)-108=0

We get rid of parentheses

x^2+9x+6x+54-108=0

We add all the numbers together, and all the variables

x^2+15x-54=0

a = 1; b = 15; c = -54;
Δ = b2-4ac
Δ = 152-4·1·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*1}=\frac{6}{2}
=3
$