(9+2x)(12+2x)=208

Solution for (9+2x)(12+2x)=208 equation:

(9+2x)(12+2x)=208

We move all terms to the left:

(9+2x)(12+2x)-(208)=0

We add all the numbers together, and all the variables

(2x+9)(2x+12)-208=0

We multiply parentheses ..

(+4x^2+24x+18x+108)-208=0

We get rid of parentheses

4x^2+24x+18x+108-208=0

We add all the numbers together, and all the variables

4x^2+42x-100=0

a = 4; b = 42; c = -100;
Δ = b2-4ac
Δ = 422-4·4·(-100)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-58}{2*4}=\frac{-100}{8}
=-12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+58}{2*4}=\frac{16}{8}
=2
$