2700/x-2700/(x+360)=2

Solution for 2700/x-2700/(x+360)=2 equation:

2700/x-2700/(x+360)=2

We move all terms to the left:

2700/x-2700/(x+360)-(2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x+360)!=0

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

x!=-360

x∈R


We calculate fractions


(2700x+972000)/(x^2+360x)+(-2700x)/(x^2+360x)-2=0

We multiply all the terms by the denominator


(2700x+972000)+(-2700x)-2*(x^2+360x)=0

We multiply parentheses

-2x^2+(2700x+972000)+(-2700x)-720x=0

We get rid of parentheses

-2x^2+2700x-2700x-720x+972000=0

We add all the numbers together, and all the variables

-2x^2-720x+972000=0

a = -2; b = -720; c = +972000;
Δ = b2-4ac
Δ = -7202-4·(-2)·972000
Δ = 8294400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8294400}=2880$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-2880}{2*-2}=\frac{-2160}{-4}
=+540
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+2880}{2*-2}=\frac{3600}{-4}
=-900
$