3/3x+1=3/4x-2

Solution for 3/3x+1=3/4x-2 equation:

3/3x+1=3/4x-2

We move all terms to the left:

3/3x+1-(3/4x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-2)!=0

x∈R


We get rid of parentheses

3/3x-3/4x+2+1=0

We calculate fractions


12x/12x^2+(-9x)/12x^2+2+1=0

We add all the numbers together, and all the variables

12x/12x^2+(-9x)/12x^2+3=0

We multiply all the terms by the denominator


12x+(-9x)+3*12x^2=0

Wy multiply elements

36x^2+12x+(-9x)=0

We get rid of parentheses

36x^2+12x-9x=0

We add all the numbers together, and all the variables

36x^2+3x=0

a = 36; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·36·0
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*36}=\frac{-6}{72}
=-1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*36}=\frac{0}{72}
=0
$