X=54+1/6x

Solution for X=54+1/6x equation:

X=54+1/6X

We move all terms to the left:

X-(54+1/6X)=0


Domain of the equation: 6X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(1/6X+54)=0

We get rid of parentheses

X-1/6X-54=0

We multiply all the terms by the denominator


X*6X-54*6X-1=0

Wy multiply elements

6X^2-324X-1=0

a = 6; b = -324; c = -1;
Δ = b2-4ac
Δ = -3242-4·6·(-1)
Δ = 105000
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:

$\sqrt{\Delta}=\sqrt{105000}=\sqrt{2500*42}=\sqrt{2500}*\sqrt{42}=50\sqrt{42}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-50\sqrt{42}}{2*6}=\frac{324-50\sqrt{42}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+50\sqrt{42}}{2*6}=\frac{324+50\sqrt{42}}{12}
$