4/x=20/3x+12

Solution for 4/x=20/3x+12 equation:

4/x=20/3x+12

We move all terms to the left:

4/x-(20/3x+12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+12)!=0

x∈R


We get rid of parentheses

4/x-20/3x-12=0

We calculate fractions


12x/3x^2+(-20x)/3x^2-12=0

We multiply all the terms by the denominator


12x+(-20x)-12*3x^2=0

Wy multiply elements

-36x^2+12x+(-20x)=0

We get rid of parentheses

-36x^2+12x-20x=0

We add all the numbers together, and all the variables

-36x^2-8x=0

a = -36; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-36)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-36}=\frac{0}{-72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-36}=\frac{16}{-72}
=-2/9
$