Solve.
-$$3 n ^ { 2 } = - 8 n - 1$$
A) $\frac { - 4 \pm \sqrt { 13 } } { 3 }$
B) $\frac { - 4 \pm \sqrt { 13 } } { 6 }$
C) $\frac { - 4 \pm \sqrt { 19 } } { 3 }$
D) $\frac { - 8 \pm \sqrt { 13 } } { 3 }$

Question

Quizplus · Accepted Answer

The equation can be rewritten as $3n^2 + 8n + 1 = 0$. Using the quadratic formula $n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 3$, $b = 8$, and $c = 1$, we find the solutions to be $\frac{-8 \pm \sqrt{64 - 12}}{6} = \frac{-8 \pm \sqrt{52}}{6} = \frac{-8 \pm \sqrt{4 \times 13}}{6} = \frac{-8 \pm 2\sqrt{13}}{6} = \frac{-4 \pm \sqrt{13}}{3}$.

Solve - 3n2=−8n−13 n ^ { 2 } = - 8 n - 13n2=−8n−1

Solve
- $3 n ^ { 2 } = - 8 n - 1$