3/7x-9=2/5x+18

Solution for 3/7x-9=2/5x+18 equation:

3/7x-9=2/5x+18

We move all terms to the left:

3/7x-9-(2/5x+18)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 5x+18)!=0

x∈R


We get rid of parentheses

3/7x-2/5x-18-9=0

We calculate fractions


15x/35x^2+(-14x)/35x^2-18-9=0

We add all the numbers together, and all the variables

15x/35x^2+(-14x)/35x^2-27=0

We multiply all the terms by the denominator


15x+(-14x)-27*35x^2=0

Wy multiply elements

-945x^2+15x+(-14x)=0

We get rid of parentheses

-945x^2+15x-14x=0

We add all the numbers together, and all the variables

-945x^2+x=0

a = -945; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-945)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-945}=\frac{-2}{-1890}
=1/945
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-945}=\frac{0}{-1890}
=0
$