(42-2x)(14-2x)=204

Solution for (42-2x)(14-2x)=204 equation:

(42-2x)(14-2x)=204

We move all terms to the left:

(42-2x)(14-2x)-(204)=0

We add all the numbers together, and all the variables

(-2x+42)(-2x+14)-204=0

We multiply parentheses ..

(+4x^2-28x-84x+588)-204=0

We get rid of parentheses

4x^2-28x-84x+588-204=0

We add all the numbers together, and all the variables

4x^2-112x+384=0

a = 4; b = -112; c = +384;
Δ = b2-4ac
Δ = -1122-4·4·384
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-80}{2*4}=\frac{32}{8}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+80}{2*4}=\frac{192}{8}
=24
$