x=54/4x

Solution for x=54/4x equation:

x=54/4x

We move all terms to the left:

x-(54/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+54/4x)=0

We get rid of parentheses

x-54/4x=0

We multiply all the terms by the denominator


x*4x-54=0

Wy multiply elements

4x^2-54=0

a = 4; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·4·(-54)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*4}=\frac{0-12\sqrt{6}}{8}
=-\frac{12\sqrt{6}}{8}
=-\frac{3\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*4}=\frac{0+12\sqrt{6}}{8}
=\frac{12\sqrt{6}}{8}
=\frac{3\sqrt{6}}{2}
$