6/13x-7=3/7x

Solution for 6/13x-7=3/7x equation:

6/13x-7=3/7x

We move all terms to the left:

6/13x-7-(3/7x)=0


Domain of the equation: 13x!=0

x!=0/13

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6/13x-(+3/7x)-7=0

We get rid of parentheses

6/13x-3/7x-7=0

We calculate fractions


42x/91x^2+(-39x)/91x^2-7=0

We multiply all the terms by the denominator


42x+(-39x)-7*91x^2=0

Wy multiply elements

-637x^2+42x+(-39x)=0

We get rid of parentheses

-637x^2+42x-39x=0

We add all the numbers together, and all the variables

-637x^2+3x=0

a = -637; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-637)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-637}=\frac{-6}{-1274}
=3/637
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-637}=\frac{0}{-1274}
=0
$