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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4x/12x^2+6x/12x^2-3+2=0

We add all the numbers together, and all the variables

4x/12x^2+6x/12x^2-1=0

We multiply all the terms by the denominator


4x+6x-1*12x^2=0

We add all the numbers together, and all the variables

10x-1*12x^2=0

Wy multiply elements

-12x^2+10x=0

a = -12; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-12)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-12}=\frac{-20}{-24}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-12}=\frac{0}{-24}
=0
$