(6+2x)(9+2x)=108

Solution for (6+2x)(9+2x)=108 equation:

(6+2x)(9+2x)=108

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+4x^2+18x+12x+54)-108=0

We get rid of parentheses

4x^2+18x+12x+54-108=0

We add all the numbers together, and all the variables

4x^2+30x-54=0

a = 4; b = 30; c = -54;
Δ = b2-4ac
Δ = 302-4·4·(-54)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-42}{2*4}=\frac{-72}{8}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+42}{2*4}=\frac{12}{8}
=1+1/2
$