240/(x+50)=240/x-5

Solution for 240/(x+50)=240/x-5 equation:

240/(x+50)=240/x-5

We move all terms to the left:

240/(x+50)-(240/x-5)=0


Domain of the equation: (x+50)!=0

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

x!=-50

x∈R



Domain of the equation: x-5)!=0

x∈R


We get rid of parentheses

240/(x+50)-240/x+5=0

We calculate fractions


240x/(x^2+50x)+(-240x-12000)/(x^2+50x)+5=0

We multiply all the terms by the denominator


240x+(-240x-12000)+5*(x^2+50x)=0

We multiply parentheses

5x^2+240x+(-240x-12000)+250x=0

We get rid of parentheses

5x^2+240x-240x+250x-12000=0

We add all the numbers together, and all the variables

5x^2+250x-12000=0

a = 5; b = 250; c = -12000;
Δ = b2-4ac
Δ = 2502-4·5·(-12000)
Δ = 302500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{302500}=550$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-550}{2*5}=\frac{-800}{10}
=-80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+550}{2*5}=\frac{300}{10}
=30
$