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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-6x)/18x^2+15x/18x^2-6-4=0

We add all the numbers together, and all the variables

(-6x)/18x^2+15x/18x^2-10=0

We multiply all the terms by the denominator


(-6x)+15x-10*18x^2=0

We add all the numbers together, and all the variables

15x+(-6x)-10*18x^2=0

Wy multiply elements

-180x^2+15x+(-6x)=0

We get rid of parentheses

-180x^2+15x-6x=0

We add all the numbers together, and all the variables

-180x^2+9x=0

a = -180; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-180)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-180}=\frac{-18}{-360}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-180}=\frac{0}{-360}
=0
$