Trying factoring, This is unfactorable, as 3 * 17 = 51, and since 17 and 3 are both prime, this means that it is impossible to find other ways to split up 51 other than 17 3, and 51, 1 so it is unfactorable.
Using the quadratic equation with a = 3, b = 9, c = 17.
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
Plugging in a b and c for a = 3, b = 9, c = 17,
\(x = {-9 \pm \sqrt{9^2-4(3)(17)} \over 2(3)}\)
This simplifies too:
\(x = {-9 \pm \sqrt{81-4(51)} \over 6}\)
Normally, since 81 - 4(51) < 0, we would say unsolvable and move on, but since complex numbers are allowed, we can continue.
\(x = {-9 \pm \sqrt{81-204} \over 6}\) = \(x = {-9 \pm \sqrt{-123} \over 6}\) = \(x = {-9 \pm (\sqrt{123})(\sqrt{-1}) \over 6}\) i = sqrt(-1), so \(x = {-9 \pm \sqrt{123}i \over 6}\)
Simplifying this to a complex number,
\(x = {\frac{-9}{6}} \pm {\sqrt{123}i \over 6} \), and simplifying the fractions, the final answer is:
\(x = {-\frac{2}{3}} \pm {\sqrt{123} \over 6 }i \)
.
