5a+9=1/a

Solution for 5a+9=1/a equation:

5a+9=1/a

We move all terms to the left:

5a+9-(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

5a-(+1/a)+9=0

We get rid of parentheses

5a-1/a+9=0

We multiply all the terms by the denominator


5a*a+9*a-1=0

We add all the numbers together, and all the variables

9a+5a*a-1=0

Wy multiply elements

5a^2+9a-1=0

a = 5; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·5·(-1)
Δ = 101
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{-(9)-\sqrt{101}}{2*5}=\frac{-9-\sqrt{101}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{101}}{2*5}=\frac{-9+\sqrt{101}}{10}
$