Question

Using the quadratic formula find the solution to $3x^{2}+18x+24=0$
$x=-2,x=-4$
$x=-4$
$x=4,x=2$
$x=-2$

Answer 1

To find the solutions for the quadratic equation \(3x^2 + 18x + 24 = 0\) using the quadratic formula, we first identify the coefficients \(a\), \(b\), and \(c\) from the general form:

\[
ax^2 + bx + c = 0
\]

For our equation:

- \(a = 3\)
- \(b = 18\)
- \(c = 24\)

The quadratic formula is given by:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Now we can calculate the discriminant \(b^2 - 4ac\):

\[
b^2 = 18^2 = 324
\]
\[
4ac = 4 \cdot 3 \cdot 24 = 288
\]
\[
b^2 - 4ac = 324 - 288 = 36
\]

Now, we substitute \(b\), \(a\), and the discriminant into the quadratic formula:

\[
x = \frac{-18 \pm \sqrt{36}}{2 \cdot 3}
\]

Calculating the square root:

\[
\sqrt{36} = 6
\]

Substituting back into the formula gives:

\[
x = \frac{-18 \pm 6}{6}
\]

Now we compute the two possible values for \(x\):

1. Using the plus sign:

\[
x = \frac{-18 + 6}{6} = \frac{-12}{6} = -2
\]

2. Using the minus sign:

\[
x = \frac{-18 - 6}{6} = \frac{-24}{6} = -4
\]

Thus, the solutions to the equation \(3x^2 + 18x + 24 = 0\) are:

\[
x = -2 \quad \text{and} \quad x = -4
\]

Therefore, the final answer is:

\[
\boxed{-2, -4}
\]