1/13x=1/39x-1

Solution for 1/13x=1/39x-1 equation:

1/13x=1/39x-1

We move all terms to the left:

1/13x-(1/39x-1)=0


Domain of the equation: 13x!=0

x!=0/13

x!=0

x∈R



Domain of the equation: 39x-1)!=0

x∈R


We get rid of parentheses

1/13x-1/39x+1=0

We calculate fractions


39x/507x^2+(-13x)/507x^2+1=0

We multiply all the terms by the denominator


39x+(-13x)+1*507x^2=0

Wy multiply elements

507x^2+39x+(-13x)=0

We get rid of parentheses

507x^2+39x-13x=0

We add all the numbers together, and all the variables

507x^2+26x=0

a = 507; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·507·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*507}=\frac{-52}{1014}
=-2/39
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*507}=\frac{0}{1014}
=0
$