x=54/5x

Solution for x=54/5x equation:

x=54/5x

We move all terms to the left:

x-(54/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+54/5x)=0

We get rid of parentheses

x-54/5x=0

We multiply all the terms by the denominator


x*5x-54=0

Wy multiply elements

5x^2-54=0

a = 5; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·5·(-54)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{30}}{2*5}=\frac{0-6\sqrt{30}}{10}
=-\frac{6\sqrt{30}}{10}
=-\frac{3\sqrt{30}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{30}}{2*5}=\frac{0+6\sqrt{30}}{10}
=\frac{6\sqrt{30}}{10}
=\frac{3\sqrt{30}}{5}
$