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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(-2x+50)(-2x+30)-5030-600=0

We add all the numbers together, and all the variables

(-2x+50)(-2x+30)-5630=0

We multiply parentheses ..

(+4x^2-60x-100x+1500)-5630=0

We get rid of parentheses

4x^2-60x-100x+1500-5630=0

We add all the numbers together, and all the variables

4x^2-160x-4130=0

a = 4; b = -160; c = -4130;
Δ = b2-4ac
Δ = -1602-4·4·(-4130)
Δ = 91680
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:

$\sqrt{\Delta}=\sqrt{91680}=\sqrt{16*5730}=\sqrt{16}*\sqrt{5730}=4\sqrt{5730}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-4\sqrt{5730}}{2*4}=\frac{160-4\sqrt{5730}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+4\sqrt{5730}}{2*4}=\frac{160+4\sqrt{5730}}{8}
$