How do you solve #a^2sqrt(3)a+1 = 0# ?
2 Answers
So we have:
Subtracting 1/4 from both sides, we get:
This has no real number solutions since the square of any real number is nonnegative.
If you want complex solutions,
Adding
I would start applying the formula to solve quadratic equations (in fact, this is a quadratic equation in "a"):
As you can see, the equation has no real solution, since it has a square root of a negative number (

So, if you are working with real numbers, the answer is that there is no
#a in RR# which makes#a^2sqrt3a+1 = 0# . 
But if you are working with complex numbers, then there are two solutions:
#a_1=(sqrt3+i)/2# and#a_2=(sqrt3i)/2# .