4800/x-4800/(x+4)=200

Solution for 4800/x-4800/(x+4)=200 equation:

4800/x-4800/(x+4)=200

We move all terms to the left:

4800/x-4800/(x+4)-(200)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x+4)!=0

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

x!=-4

x∈R


We calculate fractions


(4800x+19200)/(x^2+4x)+(-4800x)/(x^2+4x)-200=0

We multiply all the terms by the denominator


(4800x+19200)+(-4800x)-200*(x^2+4x)=0

We multiply parentheses

-200x^2+(4800x+19200)+(-4800x)-800x=0

We get rid of parentheses

-200x^2+4800x-4800x-800x+19200=0

We add all the numbers together, and all the variables

-200x^2-800x+19200=0

a = -200; b = -800; c = +19200;
Δ = b2-4ac
Δ = -8002-4·(-200)·19200
Δ = 16000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16000000}=4000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-800)-4000}{2*-200}=\frac{-3200}{-400}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-800)+4000}{2*-200}=\frac{4800}{-400}
=-12
$