3x=7x/3x-13

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

3x=7x/3x-13

We move all terms to the left:

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


Domain of the equation: 3x-13)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


3x*3x-7x+13*3x=0

We add all the numbers together, and all the variables

-7x+3x*3x+13*3x=0

Wy multiply elements

9x^2-7x+39x=0

We add all the numbers together, and all the variables

9x^2+32x=0

a = 9; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·9·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*9}=\frac{-64}{18}
=-3+5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*9}=\frac{0}{18}
=0
$