3/x+19/3x-1/3=2

Solution for 3/x+19/3x-1/3=2 equation:

3/x+19/3x-1/3=2

We move all terms to the left:

3/x+19/3x-1/3-(2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


determiningTheFunctionDomain
3/x+19/3x-2-1/3=0

We calculate fractions


81x/27x^2+19x/27x^2+(-x)/27x^2-2=0

We add all the numbers together, and all the variables

81x/27x^2+19x/27x^2+(-1x)/27x^2-2=0

We multiply all the terms by the denominator


81x+19x+(-1x)-2*27x^2=0

We add all the numbers together, and all the variables

100x+(-1x)-2*27x^2=0

Wy multiply elements

-54x^2+100x+(-1x)=0

We get rid of parentheses

-54x^2+100x-1x=0

We add all the numbers together, and all the variables

-54x^2+99x=0

a = -54; b = 99; c = 0;
Δ = b2-4ac
Δ = 992-4·(-54)·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(99)-99}{2*-54}=\frac{-198}{-108}
=1+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(99)+99}{2*-54}=\frac{0}{-108}
=0
$