Chapter 4.6, Problem 6CYU

To determine

The solutions using quadratic formula.

Answer to Problem 6CYU

The solutions are $0.33,1.5$ .

Explanation of Solution

Given:

  $22x=12x^2+6$

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,

  $\begin{array}{l}22x=12x^2+6\\ -12x^2+22x-6=0\end{array}$

So,

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ =\frac{-\left(22\right)\pm \sqrt{{\left(22\right)}^2-4\left(-12\right)\left(-6\right)}}{2\left(-12\right)}\\ =\frac{-22\pm \sqrt{196}}{-24}\\ =\frac{-22\pm 14}{-24}\\ x=\frac{-22+14}{-24}\text{or}x=\frac{-22-14}{-24}\\ x=0.33,1.5\end{array}$

Therefore,

The solutions are $0.33,1.5$ .