8a-4/a=1

Solution for 8a-4/a=1 equation:

8a-4/a=1

We move all terms to the left:

8a-4/a-(1)=0


Domain of the equation: a!=0

a∈R


We multiply all the terms by the denominator


8a*a-1*a-4=0

We add all the numbers together, and all the variables

-1a+8a*a-4=0

Wy multiply elements

8a^2-1a-4=0

a = 8; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·8·(-4)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{129}}{2*8}=\frac{1-\sqrt{129}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{129}}{2*8}=\frac{1+\sqrt{129}}{16}
$