Chapter 4, Problem 20AR

To determine

To solve the given equation, $15+4y^2=17y$ by factoring or quadratic formula.

Answer to Problem 20AR

  $x=\frac{5}{4},x=3$

Explanation of Solution

Given:

The equation is, $15+4y^2=17y$

Calculation:

We can solve the given equation by using quadratic formula.

That is,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Now, write the equation as,

  $\begin{array}{l}15+4y^2=17y\\ 4y^2-17y+15=0\end{array}$

Which is in the form of $a{x}^2+bx+c=0$ . Where, $a=4,b=-17\text{ and c = 15}$ .

Now, Substitute the values in the formula then we get that,

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-\left(-17\right)\pm \sqrt{{\left(-17\right)}^2-4\left(4\right)\left(15\right)}}{2\left(4\right)}\\ x=\frac{17\pm \sqrt{289-240}}{8}\\ x=\frac{17\pm \sqrt{49}}{8}\\ x=\frac{17\pm 7}{8}\\ x=\frac{10}{8},x=\frac{24}{8}\\ x=\frac{5}{4},x=3\end{array}$

Therefore, the roots for the given equation, $15+4y^2=17y$ are $x=\frac{5}{4},x=3$ .