6x=54/x

Solution for 6x=54/x equation:

6x=54/x

We move all terms to the left:

6x-(54/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-(+54/x)=0

We get rid of parentheses

6x-54/x=0

We multiply all the terms by the denominator


6x*x-54=0

Wy multiply elements

6x^2-54=0

a = 6; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·6·(-54)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*6}=\frac{36}{12}
=3
$