9/a=24+a

Solution for 9/a=24+a equation:

9/a=24+a

We move all terms to the left:

9/a-(24+a)=0


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

9/a-(a+24)=0

We get rid of parentheses

9/a-a-24=0

We multiply all the terms by the denominator


-a*a-24*a+9=0

We add all the numbers together, and all the variables

-24a-a*a+9=0

Wy multiply elements

-1a^2-24a+9=0

a = -1; b = -24; c = +9;
Δ = b2-4ac
Δ = -242-4·(-1)·9
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{17}}{2*-1}=\frac{24-6\sqrt{17}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{17}}{2*-1}=\frac{24+6\sqrt{17}}{-2}
$