Solve for n,
N=(n^2-9n)/20
n^2 - 9n = 20N
n^2 - 9n - 20N = 0
use the quadratic formula where
a=1
b= -9
c = 20N
thanks!
To solve for n in the equation N = (n^2 - 9n)/20, you can start by multiplying both sides of the equation by 20 to eliminate the denominator:
20N = n^2 - 9n
This gives you a quadratic equation in terms of n. Rearrange the terms and set the equation equal to zero:
n^2 - 9n - 20N = 0
To solve this quadratic equation, you can either factor or use the quadratic formula. Let's use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = -9, and c = -20N. Substitute these values into the quadratic formula:
n = (-(-9) ± √((-9)^2 - 4(1)(-20N))) / (2(1))
Simplifying further:
n = (9 ± √(81 + 80N)) / 2
Therefore, the solutions for n in terms of N are:
n = (9 + √(81 + 80N)) / 2
n = (9 - √(81 + 80N)) / 2