6x=4347/x

Solution for 6x=4347/x equation:

6x=4347/x

We move all terms to the left:

6x-(4347/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-(+4347/x)=0

We get rid of parentheses

6x-4347/x=0

We multiply all the terms by the denominator


6x*x-4347=0

Wy multiply elements

6x^2-4347=0

a = 6; b = 0; c = -4347;
Δ = b2-4ac
Δ = 02-4·6·(-4347)
Δ = 104328
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:

$\sqrt{\Delta}=\sqrt{104328}=\sqrt{324*322}=\sqrt{324}*\sqrt{322}=18\sqrt{322}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{322}}{2*6}=\frac{0-18\sqrt{322}}{12}
=-\frac{18\sqrt{322}}{12}
=-\frac{3\sqrt{322}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{322}}{2*6}=\frac{0+18\sqrt{322}}{12}
=\frac{18\sqrt{322}}{12}
=\frac{3\sqrt{322}}{2}
$