6/x+2=12/3x-3

Solution for 6/x+2=12/3x-3 equation:

6/x+2=12/3x-3

We move all terms to the left:

6/x+2-(12/3x-3)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

6/x-12/3x+3+2=0

We calculate fractions


18x/3x^2+(-12x)/3x^2+3+2=0

We add all the numbers together, and all the variables

18x/3x^2+(-12x)/3x^2+5=0

We multiply all the terms by the denominator


18x+(-12x)+5*3x^2=0

Wy multiply elements

15x^2+18x+(-12x)=0

We get rid of parentheses

15x^2+18x-12x=0

We add all the numbers together, and all the variables

15x^2+6x=0

a = 15; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·15·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*15}=\frac{-12}{30}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*15}=\frac{0}{30}
=0
$