Question

How do you solve `7n ^ { 2} + 2n = 8`?

Answer 1

`n=0.9357` and `-1.2214`

Explanation:

You first make the equation equal to zero:

`7n^2+2n =8` becomes `7n^2+2n-8=0`

Now you're equation has the form of a quadratic:
`ax^2+bx+c=0` where `a=7, b=2 and c=-8`

You can therefore use the Quadratic formula to solve for `x`:

`x=(-b±sqrt(b^2-4ac))/(2a)`

because of the `±` you will have two answers for `x`

(Just in this case the variable is `n` instead of `x`)

When you plug the number you have:
`n=(-2±sqrt(2^2-(4*7*(-8))))/(2*7)`

You simplify:
`n=(-2±sqrt(4-(-224)))/(14)`

`n=(-2±sqrt(228))/(14)`

`n=(-2±15.0997)/(14)`

This I when you will get the two different answers:

`n=(-2+15.0997)/(14)` and `x=(-2-15.0997)/(14)`

`n=13.0997/(14)` and `x=-17.0997/(14)`

Therefore

`n=0.9357` and `-1.2214`

This is proven when you take the graph of the function `7n^2+2n-8` (just plug `x` instead of `n` so the calculator is happy)

graph{7x^2+2x-8 [-5, 5, -9.1, 9.03]}
Your result corresponds to the two places where the graph of the function interests with the x-axis.