9-a=8/a

Solution for 9-a=8/a equation:

9-a=8/a

We move all terms to the left:

9-a-(8/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

-a-(+8/a)+9=0

We add all the numbers together, and all the variables

-1a-(+8/a)+9=0

We get rid of parentheses

-1a-8/a+9=0

We multiply all the terms by the denominator


-1a*a+9*a-8=0

We add all the numbers together, and all the variables

9a-1a*a-8=0

Wy multiply elements

-1a^2+9a-8=0

a = -1; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·(-1)·(-8)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7}{2*-1}=\frac{-16}{-2}
=+8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7}{2*-1}=\frac{-2}{-2}
=1
$