1/3x=x-13

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

1/3x=x-13

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-x+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 = 1533
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{1533}}{2*-3}=\frac{-39-\sqrt{1533}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{1533}}{2*-3}=\frac{-39+\sqrt{1533}}{-6}
$