1/3x-2=6-3/4x

Solution for 1/3x-2=6-3/4x equation:

1/3x-2=6-3/4x

We move all terms to the left:

1/3x-2-(6-3/4x)=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-(-3/4x+6)-2=0

We get rid of parentheses

1/3x+3/4x-6-2=0

We calculate fractions


4x/12x^2+9x/12x^2-6-2=0

We add all the numbers together, and all the variables

4x/12x^2+9x/12x^2-8=0

We multiply all the terms by the denominator


4x+9x-8*12x^2=0

We add all the numbers together, and all the variables

13x-8*12x^2=0

Wy multiply elements

-96x^2+13x=0

a = -96; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-96)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-96}=\frac{-26}{-192}
=13/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-96}=\frac{0}{-192}
=0
$