Fractions in the Answer

When a is not 1, the bottom of the formula, 2a, is no longer 2, and the parts often come out as fractions. Take $9{x}^{2}+6x+5 = 0$: a is 9, b is 6, c is 5, and ${b}^{2}-4ac$ is $36-180$, which is -144. Its root is 12i.

So $x = \frac{-6\pm12i}{18}$. Divide each term of the top by 18 and reduce: -6 over 18 is $-\frac{1}{3}$, and 12 over 18 is $\frac{2}{3}$. The solutions are $x = -\frac{1}{3}+\frac{2}{3}i$ and $x = -\frac{1}{3}-\frac{2}{3}i$.

Why divide term by term? The form $a+bi$ names the real part and the imaginary part separately, so each gets its own fraction, reduced. A common slip is to reduce one term and forget the other.