Question

Solve the equation using quadratic formula.

$4n^2-9n+5=0$

Short answer

The solutions are$n=1,n=\frac{5}{4}$.

Step-by-step solution

 Given Information. 

The given equation is$4n^2-9n+5=0$.

Write the quadratic equation in standard form and identify a,b,c.

The quadratic equation is in standard form.

So,

$a=4,b=-9,c=5$

Substitute the values in quadratic formula. 

$$\begin{gathered} n=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ n=\frac{-(-9)\pm \sqrt{(-9{)}^2-4(4\left)\right(5)}}{2\left(4\right)} \\ n=\frac{9\pm \sqrt{81-80}}{8} \\ n=\frac{9\pm \sqrt{1}}{8} \end{gathered}$$

$n=\frac{9\pm 1}{8}$

Rewrite to show two solutions. 

$$\begin{gathered} n_1=\frac{9+1}{8} \\ {n}_1=\frac{10}{8} \\ {n}_1=\frac{5}{4} \\ {n}_2=\frac{9-1}{8} \\ {n}_2=\frac{8}{8} \\ {n}_2=1 \end{gathered}$$

Thus, the solutions are$n=1,n=\frac{5}{4}$.