(14000)/(x-3)=(14000)/(x)+1500

Solution for (14000)/(x-3)=(14000)/(x)+1500 equation:

(14000)/(x-3)=(14000)/(x)+1500

We move all terms to the left:

(14000)/(x-3)-((14000)/(x)+1500)=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+1500)!=0

x∈R


We get rid of parentheses

14000/(x-3)-14000/x-1500=0

We calculate fractions


14000x/(x^2-3x)+(-14000x+42000)/(x^2-3x)-1500=0

We multiply all the terms by the denominator


14000x+(-14000x+42000)-1500*(x^2-3x)=0

We multiply parentheses

-1500x^2+14000x+(-14000x+42000)+4500x=0

We get rid of parentheses

-1500x^2+14000x-14000x+4500x+42000=0

We add all the numbers together, and all the variables

-1500x^2+4500x+42000=0

a = -1500; b = 4500; c = +42000;
Δ = b2-4ac
Δ = 45002-4·(-1500)·42000
Δ = 272250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{272250000}=16500$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4500)-16500}{2*-1500}=\frac{-21000}{-3000}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4500)+16500}{2*-1500}=\frac{12000}{-3000}
=-4
$