(3600)/(x+60)+10=(3600)/(x)

Solution for (3600)/(x+60)+10=(3600)/(x) equation:

(3600)/(x+60)+10=(3600)/(x)

We move all terms to the left:

(3600)/(x+60)+10-((3600)/(x))=0


Domain of the equation: (x+60)!=0

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

x!=-60

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3600/(x+60)-(+3600/x)+10=0

We get rid of parentheses

3600/(x+60)-3600/x+10=0

We calculate fractions


3600x/(x^2+60x)+(-3600x-216000)/(x^2+60x)+10=0

We multiply all the terms by the denominator


3600x+(-3600x-216000)+10*(x^2+60x)=0

We multiply parentheses

10x^2+3600x+(-3600x-216000)+600x=0

We get rid of parentheses

10x^2+3600x-3600x+600x-216000=0

We add all the numbers together, and all the variables

10x^2+600x-216000=0

a = 10; b = 600; c = -216000;
Δ = b2-4ac
Δ = 6002-4·10·(-216000)
Δ = 9000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9000000}=3000$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-3000}{2*10}=\frac{-3600}{20}
=-180
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+3000}{2*10}=\frac{2400}{20}
=120
$