(50-2x)(30-2x)=600

Solution for (50-2x)(30-2x)=600 equation:

(50-2x)(30-2x)=600

We move all terms to the left:

(50-2x)(30-2x)-(600)=0

We add all the numbers together, and all the variables

(-2x+50)(-2x+30)-600=0

We multiply parentheses ..

(+4x^2-60x-100x+1500)-600=0

We get rid of parentheses

4x^2-60x-100x+1500-600=0

We add all the numbers together, and all the variables

4x^2-160x+900=0

a = 4; b = -160; c = +900;
Δ = b2-4ac
Δ = -1602-4·4·900
Δ = 11200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-40\sqrt{7}}{2*4}=\frac{160-40\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+40\sqrt{7}}{2*4}=\frac{160+40\sqrt{7}}{8}
$