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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/18x^2+(-3x)/18x^2-4-5=0

We add all the numbers together, and all the variables

6x/18x^2+(-3x)/18x^2-9=0

We multiply all the terms by the denominator


6x+(-3x)-9*18x^2=0

Wy multiply elements

-162x^2+6x+(-3x)=0

We get rid of parentheses

-162x^2+6x-3x=0

We add all the numbers together, and all the variables

-162x^2+3x=0

a = -162; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-162)·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*-162}=\frac{-6}{-324}
=1/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-162}=\frac{0}{-324}
=0
$