x=1-4x/3x

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

x=1-4x/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x+4x/3x-1=0

We multiply all the terms by the denominator


x*3x+4x-1*3x=0

We add all the numbers together, and all the variables

4x+x*3x-1*3x=0

Wy multiply elements

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

We add all the numbers together, and all the variables

3x^2+x=0

a = 3; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·3·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*3}=\frac{-2}{6}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*3}=\frac{0}{6}
=0
$