(13/3x)-(4/x)=12

Solution for (13/3x)-(4/x)=12 equation:

(13/3x)-(4/x)=12

We move all terms to the left:

(13/3x)-(4/x)-(12)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+13/3x)-(+4/x)-12=0

We get rid of parentheses

13/3x-4/x-12=0

We calculate fractions


13x/3x^2+(-12x)/3x^2-12=0

We multiply all the terms by the denominator


13x+(-12x)-12*3x^2=0

Wy multiply elements

-36x^2+13x+(-12x)=0

We get rid of parentheses

-36x^2+13x-12x=0

We add all the numbers together, and all the variables

-36x^2+x=0

a = -36; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-36)·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*-36}=\frac{-2}{-72}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-36}=\frac{0}{-72}
=0
$