(200-2x)(75-2x)=10000

Solution for (200-2x)(75-2x)=10000 equation:

(200-2x)(75-2x)=10000

We move all terms to the left:

(200-2x)(75-2x)-(10000)=0

We add all the numbers together, and all the variables

(-2x+200)(-2x+75)-10000=0

We multiply parentheses ..

(+4x^2-150x-400x+15000)-10000=0

We get rid of parentheses

4x^2-150x-400x+15000-10000=0

We add all the numbers together, and all the variables

4x^2-550x+5000=0

a = 4; b = -550; c = +5000;
Δ = b2-4ac
Δ = -5502-4·4·5000
Δ = 222500
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:

$\sqrt{\Delta}=\sqrt{222500}=\sqrt{2500*89}=\sqrt{2500}*\sqrt{89}=50\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-550)-50\sqrt{89}}{2*4}=\frac{550-50\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-550)+50\sqrt{89}}{2*4}=\frac{550+50\sqrt{89}}{8}
$