Question

In the following exercises, solve by using the Quadratic Formula.$4n^2-9n+5=0$

Short answer

The solution of the quadratic equation is$n=1$and$n=\frac{5}{4}$

Step-by-step solution

Given information

We are given a quadratic equation$4n^2-9n+5=0$

Identify the values of a,b,c

On comparing with standard equation the values are$a=4,b=-9,c=5$

Write the quadratic formula and substitute the values in it

The quadratic formula can be given as

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

On substituting the values we get

$n=\frac{9\pm \sqrt{81-4\left(4\right)\left(5\right)}}{2\left(4\right)}$

Simplify

On simplifying we get

$$\begin{gathered} n=\frac{9\pm \sqrt{81-80}}{8} \\ n=\frac{9\pm \sqrt{1}}{8} \\ n=\frac{9\pm 1}{8} \end{gathered}$$

On further simplifying we get

$$\begin{gathered} n=\frac{9+1}{8} \\ n=\frac{10}{8} \\ n=\frac{5}{4} \end{gathered}$$and$$\begin{gathered} n=\frac{9-1}{8} \\ n=\frac{8}{8} \\ n=1 \end{gathered}$$

Conclusion

The solution of the quadratic equation is

$n=\frac{5}{4}$and$n=1$