2400/x-2400/(x+10)=8

Solution for 2400/x-2400/(x+10)=8 equation:

2400/x-2400/(x+10)=8

We move all terms to the left:

2400/x-2400/(x+10)-(8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: (x+10)!=0

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

x!=-10

x∈R


We calculate fractions


(2400x+24000)/(x^2+10x)+(-2400x)/(x^2+10x)-8=0

We multiply all the terms by the denominator


(2400x+24000)+(-2400x)-8*(x^2+10x)=0

We multiply parentheses

-8x^2+(2400x+24000)+(-2400x)-80x=0

We get rid of parentheses

-8x^2+2400x-2400x-80x+24000=0

We add all the numbers together, and all the variables

-8x^2-80x+24000=0

a = -8; b = -80; c = +24000;
Δ = b2-4ac
Δ = -802-4·(-8)·24000
Δ = 774400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{774400}=880$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-880}{2*-8}=\frac{-800}{-16}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+880}{2*-8}=\frac{960}{-16}
=-60
$