5/9x+1/3=5/6x

Solution for 5/9x+1/3=5/6x equation:

5/9x+1/3=5/6x

We move all terms to the left:

5/9x+1/3-(5/6x)=0


Domain of the equation: 9x!=0

x!=0/9

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

5/9x-(+5/6x)+1/3=0

We get rid of parentheses

5/9x-5/6x+1/3=0

We calculate fractions


324x^2/486x^2+270x/486x^2+(-405x)/486x^2=0

We multiply all the terms by the denominator


324x^2+270x+(-405x)=0

We get rid of parentheses

324x^2+270x-405x=0

We add all the numbers together, and all the variables

324x^2-135x=0

a = 324; b = -135; c = 0;
Δ = b2-4ac
Δ = -1352-4·324·0
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-135}{2*324}=\frac{0}{648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+135}{2*324}=\frac{270}{648}
=5/12
$