1/3x+2=37/9x

Solution for 1/3x+2=37/9x equation:

1/3x+2=37/9x

We move all terms to the left:

1/3x+2-(37/9x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(+37/9x)+2=0

We get rid of parentheses

1/3x-37/9x+2=0

We calculate fractions


9x/27x^2+(-111x)/27x^2+2=0

We multiply all the terms by the denominator


9x+(-111x)+2*27x^2=0

Wy multiply elements

54x^2+9x+(-111x)=0

We get rid of parentheses

54x^2+9x-111x=0

We add all the numbers together, and all the variables

54x^2-102x=0

a = 54; b = -102; c = 0;
Δ = b2-4ac
Δ = -1022-4·54·0
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-102}{2*54}=\frac{0}{108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+102}{2*54}=\frac{204}{108}
=1+8/9
$