3/x-1=6/3x+8

Solution for 3/x-1=6/3x+8 equation:

3/x-1=6/3x+8

We move all terms to the left:

3/x-1-(6/3x+8)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+8)!=0

x∈R


We get rid of parentheses

3/x-6/3x-8-1=0

We calculate fractions


9x/3x^2+(-6x)/3x^2-8-1=0

We add all the numbers together, and all the variables

9x/3x^2+(-6x)/3x^2-9=0

We multiply all the terms by the denominator


9x+(-6x)-9*3x^2=0

Wy multiply elements

-27x^2+9x+(-6x)=0

We get rid of parentheses

-27x^2+9x-6x=0

We add all the numbers together, and all the variables

-27x^2+3x=0

a = -27; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-27)·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*-27}=\frac{-6}{-54}
=1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-27}=\frac{0}{-54}
=0
$