49-2/3x=321/6x

Solution for 49-2/3x=321/6x equation:

49-2/3x=321/6x

We move all terms to the left:

49-2/3x-(321/6x)=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

-2/3x-(+321/6x)+49=0

We get rid of parentheses

-2/3x-321/6x+49=0

We calculate fractions


(-12x)/18x^2+(-963x)/18x^2+49=0

We multiply all the terms by the denominator


(-12x)+(-963x)+49*18x^2=0

Wy multiply elements

882x^2+(-12x)+(-963x)=0

We get rid of parentheses

882x^2-12x-963x=0

We add all the numbers together, and all the variables

882x^2-975x=0

a = 882; b = -975; c = 0;
Δ = b2-4ac
Δ = -9752-4·882·0
Δ = 950625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{950625}=975$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-975)-975}{2*882}=\frac{0}{1764}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-975)+975}{2*882}=\frac{1950}{1764}
=1+31/294
$