3/x-1=6/5x-7

Solution for 3/x-1=6/5x-7 equation:

3/x-1=6/5x-7

We move all terms to the left:

3/x-1-(6/5x-7)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x-7)!=0

x∈R


We get rid of parentheses

3/x-6/5x+7-1=0

We calculate fractions


15x/5x^2+(-6x)/5x^2+7-1=0

We add all the numbers together, and all the variables

15x/5x^2+(-6x)/5x^2+6=0

We multiply all the terms by the denominator


15x+(-6x)+6*5x^2=0

Wy multiply elements

30x^2+15x+(-6x)=0

We get rid of parentheses

30x^2+15x-6x=0

We add all the numbers together, and all the variables

30x^2+9x=0

a = 30; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·30·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*30}=\frac{-18}{60}
=-3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*30}=\frac{0}{60}
=0
$