6/a=14/2a+1

Solution for 6/a=14/2a+1 equation:

6/a=14/2a+1

We move all terms to the left:

6/a-(14/2a+1)=0


Domain of the equation: a!=0

a∈R



Domain of the equation: 2a+1)!=0

a∈R


We get rid of parentheses

6/a-14/2a-1=0

We calculate fractions


12a/2a^2+(-14a)/2a^2-1=0

We multiply all the terms by the denominator


12a+(-14a)-1*2a^2=0

Wy multiply elements

-2a^2+12a+(-14a)=0

We get rid of parentheses

-2a^2+12a-14a=0

We add all the numbers together, and all the variables

-2a^2-2a=0

a = -2; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-2)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-2}=\frac{0}{-4}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-2}=\frac{4}{-4}
=-1
$