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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


(-4x)/12x^2+(-3x)/12x^2-3+2=0

We add all the numbers together, and all the variables

(-4x)/12x^2+(-3x)/12x^2-1=0

We multiply all the terms by the denominator


(-4x)+(-3x)-1*12x^2=0

Wy multiply elements

-12x^2+(-4x)+(-3x)=0

We get rid of parentheses

-12x^2-4x-3x=0

We add all the numbers together, and all the variables

-12x^2-7x=0

a = -12; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-12)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-12}=\frac{14}{-24}
=-7/12
$