9/x=3/3x-1

Solution for 9/x=3/3x-1 equation:

9/x=3/3x-1

We move all terms to the left:

9/x-(3/3x-1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

9/x-3/3x+1=0

We calculate fractions


27x/3x^2+(-3x)/3x^2+1=0

We multiply all the terms by the denominator


27x+(-3x)+1*3x^2=0

Wy multiply elements

3x^2+27x+(-3x)=0

We get rid of parentheses

3x^2+27x-3x=0

We add all the numbers together, and all the variables

3x^2+24x=0

a = 3; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·3·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*3}=\frac{-48}{6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*3}=\frac{0}{6}
=0
$