10x-(36000/x)-48000=0

Solution for 10x-(36000/x)-48000=0 equation:

10x-(36000/x)-48000=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10x-(+36000/x)-48000=0

We get rid of parentheses

10x-36000/x-48000=0

We multiply all the terms by the denominator


10x*x-48000*x-36000=0

We add all the numbers together, and all the variables

-48000x+10x*x-36000=0

Wy multiply elements

10x^2-48000x-36000=0

a = 10; b = -48000; c = -36000;
Δ = b2-4ac
Δ = -480002-4·10·(-36000)
Δ = 2305440000
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:

$\sqrt{\Delta}=\sqrt{2305440000}=\sqrt{1440000*1601}=\sqrt{1440000}*\sqrt{1601}=1200\sqrt{1601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48000)-1200\sqrt{1601}}{2*10}=\frac{48000-1200\sqrt{1601}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48000)+1200\sqrt{1601}}{2*10}=\frac{48000+1200\sqrt{1601}}{20}
$