54/x=x*6

Solution for 54/x=x*6 equation:

54/x=x*6

We move all terms to the left:

54/x-(x*6)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

54/x-x*6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

-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
$