4/x-11=1/3x

Solution for 4/x-11=1/3x equation:

4/x-11=1/3x

We move all terms to the left:

4/x-11-(1/3x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/x-(+1/3x)-11=0

We get rid of parentheses

4/x-1/3x-11=0

We calculate fractions


12x/3x^2+(-x)/3x^2-11=0

We add all the numbers together, and all the variables

12x/3x^2+(-1x)/3x^2-11=0

We multiply all the terms by the denominator


12x+(-1x)-11*3x^2=0

Wy multiply elements

-33x^2+12x+(-1x)=0

We get rid of parentheses

-33x^2+12x-1x=0

We add all the numbers together, and all the variables

-33x^2+11x=0

a = -33; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-33)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-33}=\frac{-22}{-66}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-33}=\frac{0}{-66}
=0
$