2400/(x-3)-2400/x-40=0

Solution for 2400/(x-3)-2400/x-40=0 equation:

2400/(x-3)-2400/x-40=0


Domain of the equation: (x-3)!=0

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

x!=3

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


2400x/(x^2-3x)+(-2400x+7200)/(x^2-3x)-40=0

We multiply all the terms by the denominator


2400x+(-2400x+7200)-40*(x^2-3x)=0

We multiply parentheses

-40x^2+2400x+(-2400x+7200)+120x=0

We get rid of parentheses

-40x^2+2400x-2400x+120x+7200=0

We add all the numbers together, and all the variables

-40x^2+120x+7200=0

a = -40; b = 120; c = +7200;
Δ = b2-4ac
Δ = 1202-4·(-40)·7200
Δ = 1166400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1166400}=1080$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-1080}{2*-40}=\frac{-1200}{-80}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+1080}{2*-40}=\frac{960}{-80}
=-12
$