X-6=1/3(x)

Solution for X-6=1/3(x) equation:

X-6=1/3(X)

We move all terms to the left:

X-6-(1/3(X))=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+1/3X)-6=0

We get rid of parentheses

X-1/3X-6=0

We multiply all the terms by the denominator


X*3X-6*3X-1=0

Wy multiply elements

3X^2-18X-1=0

a = 3; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·3·(-1)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{21}}{2*3}=\frac{18-4\sqrt{21}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{21}}{2*3}=\frac{18+4\sqrt{21}}{6}
$