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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


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

We calculate fractions


12x/162x^2+(-135x)/162x^2+(-6x)/162x^2-3=0

We multiply all the terms by the denominator


12x+(-135x)+(-6x)-3*162x^2=0

Wy multiply elements

-486x^2+12x+(-135x)+(-6x)=0

We get rid of parentheses

-486x^2+12x-135x-6x=0

We add all the numbers together, and all the variables

-486x^2-129x=0

a = -486; b = -129; c = 0;
Δ = b2-4ac
Δ = -1292-4·(-486)·0
Δ = 16641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16641}=129$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-129)-129}{2*-486}=\frac{0}{-972}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-129)+129}{2*-486}=\frac{258}{-972}
=-43/162
$