4x/3x-12=1/x-4

Solution for 4x/3x-12=1/x-4 equation:

4x/3x-12=1/x-4

We move all terms to the left:

4x/3x-12-(1/x-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

4x/3x-1/x+4-12=0

We calculate fractions


4x^2/3x^2+(-3x)/3x^2+4-12=0

We add all the numbers together, and all the variables

4x^2/3x^2+(-3x)/3x^2-8=0

We multiply all the terms by the denominator


4x^2+(-3x)-8*3x^2=0

Wy multiply elements

4x^2-24x^2+(-3x)=0

We get rid of parentheses

4x^2-24x^2-3x=0

We add all the numbers together, and all the variables

-20x^2-3x=0

a = -20; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-20)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-20}=\frac{6}{-40}
=-3/20
$