9+5a=54/a=

Solution for 9+5a=54/a= equation:

9+5a=54/a=

We move all terms to the left:

9+5a-(54/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-(+54/a)+9=0

We get rid of parentheses

5a-54/a+9=0

We multiply all the terms by the denominator


5a*a+9*a-54=0

We add all the numbers together, and all the variables

9a+5a*a-54=0

Wy multiply elements

5a^2+9a-54=0

a = 5; b = 9; c = -54;
Δ = b2-4ac
Δ = 92-4·5·(-54)
Δ = 1161
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:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{129}}{2*5}=\frac{-9-3\sqrt{129}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{129}}{2*5}=\frac{-9+3\sqrt{129}}{10}
$