300-6x=2400/x

Solution for 300-6x=2400/x equation:

300-6x=2400/x

We move all terms to the left:

300-6x-(2400/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

-6x-(+2400/x)+300=0

We get rid of parentheses

-6x-2400/x+300=0

We multiply all the terms by the denominator


-6x*x+300*x-2400=0

We add all the numbers together, and all the variables

300x-6x*x-2400=0

Wy multiply elements

-6x^2+300x-2400=0

a = -6; b = 300; c = -2400;
Δ = b2-4ac
Δ = 3002-4·(-6)·(-2400)
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-180}{2*-6}=\frac{-480}{-12}
=+40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+180}{2*-6}=\frac{-120}{-12}
=+10
$