6000/x-6000(x+4)=5

Solution for 6000/x-6000(x+4)=5 equation:

6000/x-6000(x+4)=5

We move all terms to the left:

6000/x-6000(x+4)-(5)=0


Domain of the equation: x!=0

x∈R


We multiply parentheses

6000/x-6000x-24000-5=0

We multiply all the terms by the denominator


-6000x*x-24000*x-5*x+6000=0

We add all the numbers together, and all the variables

-24005x-6000x*x+6000=0

Wy multiply elements

-6000x^2-24005x+6000=0

a = -6000; b = -24005; c = +6000;
Δ = b2-4ac
Δ = -240052-4·(-6000)·6000
Δ = 720240025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{720240025}=\sqrt{25*28809601}=\sqrt{25}*\sqrt{28809601}=5\sqrt{28809601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24005)-5\sqrt{28809601}}{2*-6000}=\frac{24005-5\sqrt{28809601}}{-12000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24005)+5\sqrt{28809601}}{2*-6000}=\frac{24005+5\sqrt{28809601}}{-12000}
$