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

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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 $

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