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

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

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

We move all terms to the left:

7/9x-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-3-3=0

We calculate fractions


42x/54x^2+(-9x)/54x^2-3-3=0

We add all the numbers together, and all the variables

42x/54x^2+(-9x)/54x^2-6=0

We multiply all the terms by the denominator


42x+(-9x)-6*54x^2=0

Wy multiply elements

-324x^2+42x+(-9x)=0

We get rid of parentheses

-324x^2+42x-9x=0

We add all the numbers together, and all the variables

-324x^2+33x=0

a = -324; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-324)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-324}=\frac{-66}{-648}
=11/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-324}=\frac{0}{-648}
=0
$