Question

use the quadratic formula to solve for x.
3x² + 9x + 4 = 0
(if there is more than one solution, separate them with commas.)
x =

Explanation:

Step1: Identify coefficients

For the quadratic equation $3x^{2}+9x + 4=0$, we have $a = 3$, $b = 9$, $c = 4$.

Step2: Write quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Substitute values

Substitute $a = 3$, $b = 9$, $c = 4$ into the formula:
\[

$$\begin{align*} x&=\frac{-9\pm\sqrt{9^{2}-4\times3\times4}}{2\times3}\\ &=\frac{-9\pm\sqrt{81 - 48}}{6}\\ &=\frac{-9\pm\sqrt{33}}{6} \end{align*}$$

\]

Answer:

$x=\frac{-9+\sqrt{33}}{6},\frac{-9 - \sqrt{33}}{6}$