120x=27000/x

Solution for 120x=27000/x equation:

120x=27000/x

We move all terms to the left:

120x-(27000/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

120x-(+27000/x)=0

We get rid of parentheses

120x-27000/x=0

We multiply all the terms by the denominator


120x*x-27000=0

Wy multiply elements

120x^2-27000=0

a = 120; b = 0; c = -27000;
Δ = b2-4ac
Δ = 02-4·120·(-27000)
Δ = 12960000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12960000}=3600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3600}{2*120}=\frac{-3600}{240}
=-15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3600}{2*120}=\frac{3600}{240}
=15
$