-5/6x-1/9x=-1/2

Solution for -5/6x-1/9x=-1/2 equation:

-5/6x-1/9x=-1/2

We move all terms to the left:

-5/6x-1/9x-(-1/2)=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 get rid of parentheses

-5/6x-1/9x+1/2=0

We calculate fractions


486x^2/216x^2+(-180x)/216x^2+(-24x)/216x^2=0

We multiply all the terms by the denominator


486x^2+(-180x)+(-24x)=0

We get rid of parentheses

486x^2-180x-24x=0

We add all the numbers together, and all the variables

486x^2-204x=0

a = 486; b = -204; c = 0;
Δ = b2-4ac
Δ = -2042-4·486·0
Δ = 41616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41616}=204$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-204}{2*486}=\frac{0}{972}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+204}{2*486}=\frac{408}{972}
=34/81
$