Chapter 4.6, Problem 16PPS

To determine

The solutions using quadratic formula.

Answer to Problem 16PPS

The solutions are $1.72,-0.38$ .

Explanation of Solution

Given:

  $3x^2-4x-8=-6$

Calculation:

Quadratic formula equation,

  $\begin{array}{l}a{x}^2+bx+c=0,\\ x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\end{array}$

Now,

  $\begin{array}{l}3x^2-4x-8=-6\\ 3x^2-4x-8+6=0\\ 3x^2-4x-2=0\end{array}$

So,

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-\left(-4\right)\pm \sqrt{{\left(-4\right)}^2-4\left(3\right)\left(-2\right)}}{2\left(3\right)}\\ =\frac{4\pm \sqrt{40}}{6}\\ =\frac{4\pm 6.32}{6}\\ x=\frac{4+6.32}{6}\text{or}x=\frac{4-6.32}{6}\\ x=1.72,-0.38\end{array}$

Therefore,

The solutions are $1.72,-0.38$ .