3/x+1=7/3x-3

Solution for 3/x+1=7/3x-3 equation:

3/x+1=7/3x-3

We move all terms to the left:

3/x+1-(7/3x-3)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


9x/3x^2+(-7x)/3x^2+3+1=0

We add all the numbers together, and all the variables

9x/3x^2+(-7x)/3x^2+4=0

We multiply all the terms by the denominator


9x+(-7x)+4*3x^2=0

Wy multiply elements

12x^2+9x+(-7x)=0

We get rid of parentheses

12x^2+9x-7x=0

We add all the numbers together, and all the variables

12x^2+2x=0

a = 12; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·12·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*12}=\frac{-4}{24}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*12}=\frac{0}{24}
=0
$