a-1/a=8

Solution for a-1/a=8 equation:

a-1/a=8

We move all terms to the left:

a-1/a-(8)=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


a*a-8*a-1=0

We add all the numbers together, and all the variables

-8a+a*a-1=0

Wy multiply elements

a^2-8a-1=0

a = 1; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·1·(-1)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{17}}{2*1}=\frac{8-2\sqrt{17}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{17}}{2*1}=\frac{8+2\sqrt{17}}{2}
$