Question

What is the positive solution to this equation?




4x2+12x = 135



Record your answer below.

Answer 1

To solve the equation \(4x^2 + 12x = 135\), we first rearrange it into standard quadratic form:

\[
4x^2 + 12x - 135 = 0
\]

Next, we can use the quadratic formula, which is given by:

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

In our equation, the coefficients are:

- \(a = 4\)
- \(b = 12\)
- \(c = -135\)

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

\[
b^2 = 12^2 = 144
\]
\[
4ac = 4 \cdot 4 \cdot (-135) = -2160
\]
\[
b^2 - 4ac = 144 + 2160 = 2304
\]

Now we substitute back into the quadratic formula:

\[
x = \frac{-12 \pm \sqrt{2304}}{2 \cdot 4}
\]

Calculating \(\sqrt{2304}\):

\[
\sqrt{2304} = 48
\]

Now substituting that into the quadratic formula:

\[
x = \frac{-12 \pm 48}{8}
\]

This gives us two solutions:

1. Positive solution:
\[
x = \frac{-12 + 48}{8} = \frac{36}{8} = 4.5
\]

2. Negative solution:
\[
x = \frac{-12 - 48}{8} = \frac{-60}{8} = -7.5
\]

The positive solution is:

\[
\boxed{4.5}
\]