(12-2x)(19-2x)=144

Solution for (12-2x)(19-2x)=144 equation:

(12-2x)(19-2x)=144

We move all terms to the left:

(12-2x)(19-2x)-(144)=0

We add all the numbers together, and all the variables

(-2x+12)(-2x+19)-144=0

We multiply parentheses ..

(+4x^2-38x-24x+228)-144=0

We get rid of parentheses

4x^2-38x-24x+228-144=0

We add all the numbers together, and all the variables

4x^2-62x+84=0

a = 4; b = -62; c = +84;
Δ = b2-4ac
Δ = -622-4·4·84
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-50}{2*4}=\frac{12}{8}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+50}{2*4}=\frac{112}{8}
=14
$