(40-2x)(30-2x)=600

Solution for (40-2x)(30-2x)=600 equation:

(40-2x)(30-2x)=600

We move all terms to the left:

(40-2x)(30-2x)-(600)=0

We add all the numbers together, and all the variables

(-2x+40)(-2x+30)-600=0

We multiply parentheses ..

(+4x^2-60x-80x+1200)-600=0

We get rid of parentheses

4x^2-60x-80x+1200-600=0

We add all the numbers together, and all the variables

4x^2-140x+600=0

a = 4; b = -140; c = +600;
Δ = b2-4ac
Δ = -1402-4·4·600
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-100}{2*4}=\frac{40}{8}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+100}{2*4}=\frac{240}{8}
=30
$