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

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

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

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 14x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


14x/98x^2+(-21x)/98x^2-1-2=0

We add all the numbers together, and all the variables

14x/98x^2+(-21x)/98x^2-3=0

We multiply all the terms by the denominator


14x+(-21x)-3*98x^2=0

Wy multiply elements

-294x^2+14x+(-21x)=0

We get rid of parentheses

-294x^2+14x-21x=0

We add all the numbers together, and all the variables

-294x^2-7x=0

a = -294; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-294)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-294}=\frac{0}{-588}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-294}=\frac{14}{-588}
=-1/42
$