7/9x-2/3=1/6x+3

Solution for 7/9x-2/3=1/6x+3 equation:

7/9x-2/3=1/6x+3

We move all terms to the left:

7/9x-2/3-(1/6x+3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 6x+3)!=0

x∈R


We get rid of parentheses

7/9x-1/6x-3-2/3=0

We calculate fractions


(-648x^2)/486x^2+378x/486x^2+(-81x)/486x^2-3=0

We multiply all the terms by the denominator


(-648x^2)+378x+(-81x)-3*486x^2=0

Wy multiply elements

(-648x^2)-1458x^2+378x+(-81x)=0

We get rid of parentheses

-648x^2-1458x^2+378x-81x=0

We add all the numbers together, and all the variables

-2106x^2+297x=0

a = -2106; b = 297; c = 0;
Δ = b2-4ac
Δ = 2972-4·(-2106)·0
Δ = 88209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{88209}=297$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(297)-297}{2*-2106}=\frac{-594}{-4212}
=11/78
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(297)+297}{2*-2106}=\frac{0}{-4212}
=0
$