7/6x-2/3=4/7x

Solution for 7/6x-2/3=4/7x equation:

7/6x-2/3=4/7x

We move all terms to the left:

7/6x-2/3-(4/7x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/6x-(+4/7x)-2/3=0

We get rid of parentheses

7/6x-4/7x-2/3=0

We calculate fractions


(-588x^2)/378x^2+441x/378x^2+(-216x)/378x^2=0

We multiply all the terms by the denominator


(-588x^2)+441x+(-216x)=0

We get rid of parentheses

-588x^2+441x-216x=0

We add all the numbers together, and all the variables

-588x^2+225x=0

a = -588; b = 225; c = 0;
Δ = b2-4ac
Δ = 2252-4·(-588)·0
Δ = 50625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{50625}=225$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(225)-225}{2*-588}=\frac{-450}{-1176}
=75/196
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(225)+225}{2*-588}=\frac{0}{-1176}
=0
$