(20-2x)(15-2x)=234

Solution for (20-2x)(15-2x)=234 equation:

(20-2x)(15-2x)=234

We move all terms to the left:

(20-2x)(15-2x)-(234)=0

We add all the numbers together, and all the variables

(-2x+20)(-2x+15)-234=0

We multiply parentheses ..

(+4x^2-30x-40x+300)-234=0

We get rid of parentheses

4x^2-30x-40x+300-234=0

We add all the numbers together, and all the variables

4x^2-70x+66=0

a = 4; b = -70; c = +66;
Δ = b2-4ac
Δ = -702-4·4·66
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-62}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+62}{2*4}=\frac{132}{8}
=16+1/2
$