7/9x-13/6x=1/12

Solution for 7/9x-13/6x=1/12 equation:

7/9x-13/6x=1/12

We move all terms to the left:

7/9x-13/6x-(1/12)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

7/9x-13/6x-(+1/12)=0

We get rid of parentheses

7/9x-13/6x-1/12=0

We calculate fractions


(-324x^2)/648x^2+504x/648x^2+(-1404x)/648x^2=0

We multiply all the terms by the denominator


(-324x^2)+504x+(-1404x)=0

We get rid of parentheses

-324x^2+504x-1404x=0

We add all the numbers together, and all the variables

-324x^2-900x=0

a = -324; b = -900; c = 0;
Δ = b2-4ac
Δ = -9002-4·(-324)·0
Δ = 810000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{810000}=900$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-900}{2*-324}=\frac{0}{-648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+900}{2*-324}=\frac{1800}{-648}
=-2+7/9
$