x=x^2/3600-50x

Solution for x=x^2/3600-50x equation:

x=x^2/3600-50x

We move all terms to the left:

x-(x^2/3600-50x)=0


Domain of the equation: 3600-50x)!=0

We move all terms containing x to the left, all other terms to the right

-50x)!=-3600

x!=-3600/1

x!=-3600

x∈R


We get rid of parentheses

-x^2/3600+x+50x=0

We multiply all the terms by the denominator


-x^2+x*3600+50x*3600=0

We add all the numbers together, and all the variables

-1x^2+x*3600+50x*3600=0

Wy multiply elements

-1x^2+3600x+180000x=0

We add all the numbers together, and all the variables

-1x^2+183600x=0

a = -1; b = 183600; c = 0;
Δ = b2-4ac
Δ = 1836002-4·(-1)·0
Δ = 33708960000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{33708960000}=183600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(183600)-183600}{2*-1}=\frac{-367200}{-2}
=+183600
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(183600)+183600}{2*-1}=\frac{0}{-2}
=0
$