9/7x=13/14x+2

Solution for 9/7x=13/14x+2 equation:

9/7x=13/14x+2

We move all terms to the left:

9/7x-(13/14x+2)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 14x+2)!=0

x∈R


We get rid of parentheses

9/7x-13/14x-2=0

We calculate fractions


126x/98x^2+(-91x)/98x^2-2=0

We multiply all the terms by the denominator


126x+(-91x)-2*98x^2=0

Wy multiply elements

-196x^2+126x+(-91x)=0

We get rid of parentheses

-196x^2+126x-91x=0

We add all the numbers together, and all the variables

-196x^2+35x=0

a = -196; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-196)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-196}=\frac{-70}{-392}
=5/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-196}=\frac{0}{-392}
=0
$