1/6x-4=5/3x

Solution for 1/6x-4=5/3x equation:

1/6x-4=5/3x

We move all terms to the left:

1/6x-4-(5/3x)=0


Domain of the equation: 6x!=0

x!=0/6

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

1/6x-(+5/3x)-4=0

We get rid of parentheses

1/6x-5/3x-4=0

We calculate fractions


3x/18x^2+(-30x)/18x^2-4=0

We multiply all the terms by the denominator


3x+(-30x)-4*18x^2=0

Wy multiply elements

-72x^2+3x+(-30x)=0

We get rid of parentheses

-72x^2+3x-30x=0

We add all the numbers together, and all the variables

-72x^2-27x=0

a = -72; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-72)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-72}=\frac{0}{-144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-72}=\frac{54}{-144}
=-3/8
$