This is tricky equation and simply making algebraic manipulations will require a lot of work.
In fact this equation doesn't have real roots.
Let's see why.
First of all domain of this equation is x>0.
Next. It is known that for a>0 and b>0
Proof is straightforward. -> -> .
Therefore, left side is greater or equal than 6 for all x>0.
Now, let's see how to handle right part.
Take expression and complete the square:
From this we have that for all x.
Now, divide this expression by 4: or .
Finally we have that
Dividing by (it is positive for all values of x) gives
Taking square roots and remembering that x>0 yields
So, what did we show?
We showed that left part is at least 6 and right part is less than 5.5. There are no intersections, so equation has no real roots.