(200-10x)(90+5x)=17600

Solution for (200-10x)(90+5x)=17600 equation:

(200-10x)(90+5x)=17600

We move all terms to the left:

(200-10x)(90+5x)-(17600)=0

We add all the numbers together, and all the variables

(-10x+200)(5x+90)-17600=0

We multiply parentheses ..

(-50x^2-900x+1000x+18000)-17600=0

We get rid of parentheses

-50x^2-900x+1000x+18000-17600=0

We add all the numbers together, and all the variables

-50x^2+100x+400=0

a = -50; b = 100; c = +400;
Δ = b2-4ac
Δ = 1002-4·(-50)·400
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-300}{2*-50}=\frac{-400}{-100}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+300}{2*-50}=\frac{200}{-100}
=-2
$