Question

Solve the quadratic equations below. Use any method you want.

$3n^2+8n+3=0$

Short answer

As a result, the two solutions are$n=\frac{-4-\sqrt{7}}{3}$ and$n=\frac{-4+\sqrt{7}}{3}$.

Step-by-step solution

Given information.

The given equation is

$3n^2+8n+3=0$

Step 2. Use the quadratic formula to solve the equation.

First, write the equation $a{x}^2+bx+c=0$in standard form, as shown below.

This is already done in this place.

Determine the a, b, and c values.

When compared to the standard, the values are a = 3 b = 8 and c= 3.

In the quadratic formula, substitute a=3,b=8, and c= 3.

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

role="math" localid="1653847814613" $n=\frac{8\pm \sqrt{{\left(8\right)}^2-4\left(3\right)\left(3\right)}}{2\left(3\right)}$

As shown below, simplify the fraction.

$$\begin{gathered} n=\frac{-8\pm \sqrt{{\left(8\right)}^2-4\left(3\right)\left(3\right)}}{2\left(3\right)} \\ n=\frac{-8\pm \sqrt{64-36}}{6} \\ n=\frac{-8\pm \sqrt{28}}{6} \\ \frac{n=-4\pm 2\sqrt{7}}{3} \end{gathered}$$

As a result, the two solutions are $n=\frac{-4-\sqrt{7}}{3}$ and $\frac{n=-4+\sqrt{7}}{3}$.