1/3x=13-x

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

1/3x=13-x

We move all terms to the left:

1/3x-(13-x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/3x+1x-13=0

We multiply all the terms by the denominator


1x*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}
$