Question

question
use the quadratic formula to solve. express your answer in simplest form.
$5n^2 - 30n + 20 = -n$

Explanation:

Step1: Rewrite to standard quadratic form

$5n^2 - 30n + 20 + n = 0$
$5n^2 - 29n + 20 = 0$

Step2: Identify a, b, c values

For $ax^2+bx+c=0$, $a=5$, $b=-29$, $c=20$

Step3: Substitute into quadratic formula

Quadratic formula: $n=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$n=\frac{-(-29)\pm\sqrt{(-29)^2-4(5)(20)}}{2(5)}$

Step4: Calculate discriminant

$\sqrt{841 - 400}=\sqrt{441}=21$

Step5: Simplify to find solutions

$n=\frac{29\pm21}{10}$

Answer:

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