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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4x^2/27x^2+(-27x)/27x^2+(-x)/27x^2=0

We add all the numbers together, and all the variables

4x^2/27x^2+(-27x)/27x^2+(-1x)/27x^2=0

We multiply all the terms by the denominator


4x^2+(-27x)+(-1x)=0

We get rid of parentheses

4x^2-27x-1x=0

We add all the numbers together, and all the variables

4x^2-28x=0

a = 4; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·4·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*4}=\frac{56}{8}
=7
$