7a=2+1/a

Solution for 7a=2+1/a equation:

7a=2+1/a

We move all terms to the left:

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


Domain of the equation: a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

7a-1/a-2=0

We multiply all the terms by the denominator


7a*a-2*a-1=0

We add all the numbers together, and all the variables

-2a+7a*a-1=0

Wy multiply elements

7a^2-2a-1=0

a = 7; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·7·(-1)
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{2}}{2*7}=\frac{2-4\sqrt{2}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{2}}{2*7}=\frac{2+4\sqrt{2}}{14}
$