Dividing by variable when solving algebraic equation

[robvalue]

No worries, so easily done

For the general equation

ax^2 + bx + c = 0

where a isn't zero, and a, b and c are real numbers:

you can calculate the value of

d = b^2 - 4ac

When d > 0 you have two real solutions
When d = 0 you have one real solution
When d < 0 you have two complex solutions

The solution(s) are given by

x = [ -b + sqrt(d) ] / 2a

and

x = [ -b - sqrt(d) ] / 2a

sqrt is square root. As you can see, when d = 0, these two solutions are the same. When d < 0 we're taking the square root of a negative number, and as such the result will be complex.

[If you allow a, b and c to be complex the solution formulae still work.]