4/x+4/3x=x/3

Solution for 4/x+4/3x=x/3 equation:

4/x+4/3x=x/3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-1x^2)/27x^2+108x/27x^2+4x/27x^2=0

We multiply all the terms by the denominator


(-1x^2)+108x+4x=0

We add all the numbers together, and all the variables

(-1x^2)+112x=0

We get rid of parentheses

-1x^2+112x=0

a = -1; b = 112; c = 0;
Δ = b2-4ac
Δ = 1122-4·(-1)·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-112}{2*-1}=\frac{-224}{-2}
=+112
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+112}{2*-1}=\frac{0}{-2}
=0
$