6/2=a-8/a-1

Solution for 6/2=a-8/a-1 equation:

6/2=a-8/a-1

We move all terms to the left:

6/2-(a-8/a-1)=0


Domain of the equation: a-1)!=0

a∈R


We add all the numbers together, and all the variables

-(a-8/a-1)+3=0

We get rid of parentheses

-a+8/a+1+3=0

We multiply all the terms by the denominator


-a*a+1*a+3*a+8=0

We add all the numbers together, and all the variables

4a-a*a+8=0

Wy multiply elements

-1a^2+4a+8=0

a = -1; b = 4; c = +8;
Δ = b2-4ac
Δ = 42-4·(-1)·8
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{3}}{2*-1}=\frac{-4-4\sqrt{3}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{3}}{2*-1}=\frac{-4+4\sqrt{3}}{-2}
$