3/4x-6/7=5/9x=1/7

Solution for 3/4x-6/7=5/9x=1/7 equation:

3/4x-6/7=5/9x=1/7

We move all terms to the left:

3/4x-6/7-(5/9x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(+5/9x)-6/7=0

We get rid of parentheses

3/4x-5/9x-6/7=0

We calculate fractions


(-1944x^2)/1764x^2+1323x/1764x^2+(-980x)/1764x^2=0

We multiply all the terms by the denominator


(-1944x^2)+1323x+(-980x)=0

We get rid of parentheses

-1944x^2+1323x-980x=0

We add all the numbers together, and all the variables

-1944x^2+343x=0

a = -1944; b = 343; c = 0;
Δ = b2-4ac
Δ = 3432-4·(-1944)·0
Δ = 117649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{117649}=343$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(343)-343}{2*-1944}=\frac{-686}{-3888}
=343/1944
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(343)+343}{2*-1944}=\frac{0}{-3888}
=0
$