-5/6x+7/9x-4/9=-1/2

Solution for -5/6x+7/9x-4/9=-1/2 equation:

-5/6x+7/9x-4/9=-1/2

We move all terms to the left:

-5/6x+7/9x-4/9-(-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+7/9x-4/9+1/2=0

We calculate fractions


4374x^2/8748x^2+(-7290x)/8748x^2+168x/8748x^2+(-96x)/8748x^2=0

We multiply all the terms by the denominator


4374x^2+(-7290x)+168x+(-96x)=0

We add all the numbers together, and all the variables

4374x^2+168x+(-7290x)+(-96x)=0

We get rid of parentheses

4374x^2+168x-7290x-96x=0

We add all the numbers together, and all the variables

4374x^2-7218x=0

a = 4374; b = -7218; c = 0;
Δ = b2-4ac
Δ = -72182-4·4374·0
Δ = 52099524
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{52099524}=7218$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7218)-7218}{2*4374}=\frac{0}{8748}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7218)+7218}{2*4374}=\frac{14436}{8748}
=1+158/243
$