5/6x-4/9x=1/3

Solution for 5/6x-4/9x=1/3 equation:

5/6x-4/9x=1/3

We move all terms to the left:

5/6x-4/9x-(1/3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x-4/9x-(+1/3)=0

We get rid of parentheses

5/6x-4/9x-1/3=0

We calculate fractions


(-486x^2)/486x^2+405x/486x^2+(-216x)/486x^2=0

We multiply all the terms by the denominator


(-486x^2)+405x+(-216x)=0

We get rid of parentheses

-486x^2+405x-216x=0

We add all the numbers together, and all the variables

-486x^2+189x=0

a = -486; b = 189; c = 0;
Δ = b2-4ac
Δ = 1892-4·(-486)·0
Δ = 35721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35721}=189$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(189)-189}{2*-486}=\frac{-378}{-972}
=7/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(189)+189}{2*-486}=\frac{0}{-972}
=0
$