X=13-1/3x

Solution for X=13-1/3x equation:

X=13-1/3X

We move all terms to the left:

X-(13-1/3X)=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+13)=0

We get rid of parentheses

X+1/3X-13=0

We multiply all the terms by the denominator


X*3X-13*3X+1=0

Wy multiply elements

3X^2-39X+1=0

a = 3; b = -39; c = +1;
Δ = b2-4ac
Δ = -392-4·3·1
Δ = 1509
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1509}}{2*3}=\frac{39-\sqrt{1509}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1509}}{2*3}=\frac{39+\sqrt{1509}}{6}
$