1/3x-4=3/4x

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

1/3x-4=3/4x

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


4x/12x^2+(-9x)/12x^2-4=0

We multiply all the terms by the denominator


4x+(-9x)-4*12x^2=0

Wy multiply elements

-48x^2+4x+(-9x)=0

We get rid of parentheses

-48x^2+4x-9x=0

We add all the numbers together, and all the variables

-48x^2-5x=0

a = -48; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-48)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-48}=\frac{10}{-96}
=-5/48
$