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

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

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

We move all terms to the left:

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


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R



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

a∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-294a^2-7a=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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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