(23-2x)(20-2x)=130

Solution for (23-2x)(20-2x)=130 equation:

(23-2x)(20-2x)=130

We move all terms to the left:

(23-2x)(20-2x)-(130)=0

We add all the numbers together, and all the variables

(-2x+23)(-2x+20)-130=0

We multiply parentheses ..

(+4x^2-40x-46x+460)-130=0

We get rid of parentheses

4x^2-40x-46x+460-130=0

We add all the numbers together, and all the variables

4x^2-86x+330=0

a = 4; b = -86; c = +330;
Δ = b2-4ac
Δ = -862-4·4·330
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-46}{2*4}=\frac{40}{8}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+46}{2*4}=\frac{132}{8}
=16+1/2
$