Question

One-half the sum of a number and four is three less than the quotient of five and the number.

Answer 1

12 ( n + 4 ) = 5/n - 3

Answer 2

Let the number be x.

`(1)/(2)(x+4)=(5)/(x)-3\\\\x+4=(10)/(x)-6\\\\x+10=(10)/(x)\\\\x^2-(10)/(x)+10=0\\\\(x^2+10x-10)/(x)=0\\\\ x\\eq0\\\\x^2+10x-10=0\\\\ x=(-10\pm √(10^2-4 * (-10)))/(2* 1)\\\\x=(-10 \pm √(140))/(2)`

For a Quadratic equation of the form

Ax²+Bx+c=0

D=B²-4AC

`x=(-B \pm √(D))/(2A)`