(200-2x)(x+5)=200x

Solution for (200-2x)(x+5)=200x equation:

(200-2x)(x+5)=200x

We move all terms to the left:

(200-2x)(x+5)-(200x)=0

We add all the numbers together, and all the variables

(-2x+200)(x+5)-200x=0

We add all the numbers together, and all the variables

-200x+(-2x+200)(x+5)=0

We multiply parentheses ..

(-2x^2-10x+200x+1000)-200x=0

We get rid of parentheses

-2x^2-10x+200x-200x+1000=0

We add all the numbers together, and all the variables

-2x^2-10x+1000=0

a = -2; b = -10; c = +1000;
Δ = b2-4ac
Δ = -102-4·(-2)·1000
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-90}{2*-2}=\frac{-80}{-4}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+90}{2*-2}=\frac{100}{-4}
=-25
$