2/7x-9=1/14x-3

Solution for 2/7x-9=1/14x-3 equation:

2/7x-9=1/14x-3

We move all terms to the left:

2/7x-9-(1/14x-3)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 14x-3)!=0

x∈R


We get rid of parentheses

2/7x-1/14x+3-9=0

We calculate fractions


28x/98x^2+(-7x)/98x^2+3-9=0

We add all the numbers together, and all the variables

28x/98x^2+(-7x)/98x^2-6=0

We multiply all the terms by the denominator


28x+(-7x)-6*98x^2=0

Wy multiply elements

-588x^2+28x+(-7x)=0

We get rid of parentheses

-588x^2+28x-7x=0

We add all the numbers together, and all the variables

-588x^2+21x=0

a = -588; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-588)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-588}=\frac{-42}{-1176}
=1/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-588}=\frac{0}{-1176}
=0
$