5/6x-1/2-2/3x=4/3

Solution for 5/6x-1/2-2/3x=4/3 equation:

5/6x-1/2-2/3x=4/3

We move all terms to the left:

5/6x-1/2-2/3x-(4/3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-2/3x-1/2-(+4/3)=0

We get rid of parentheses

5/6x-2/3x-1/2-4/3=0

We calculate fractions


(-162x^2)/216x^2+180x/216x^2+(-48x)/216x^2+(-96x)/216x^2=0

We multiply all the terms by the denominator


(-162x^2)+180x+(-48x)+(-96x)=0

We get rid of parentheses

-162x^2+180x-48x-96x=0

We add all the numbers together, and all the variables

-162x^2+36x=0

a = -162; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-162)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-162}=\frac{-72}{-324}
=2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-162}=\frac{0}{-324}
=0
$