(20+2x)(12+2x)=468

Solution for (20+2x)(12+2x)=468 equation:

(20+2x)(12+2x)=468

We move all terms to the left:

(20+2x)(12+2x)-(468)=0

We add all the numbers together, and all the variables

(2x+20)(2x+12)-468=0

We multiply parentheses ..

(+4x^2+24x+40x+240)-468=0

We get rid of parentheses

4x^2+24x+40x+240-468=0

We add all the numbers together, and all the variables

4x^2+64x-228=0

a = 4; b = 64; c = -228;
Δ = b2-4ac
Δ = 642-4·4·(-228)
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-88}{2*4}=\frac{-152}{8}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+88}{2*4}=\frac{24}{8}
=3
$