Question

How do you solve `9y^2+16= -24`?

Answer 1

I am not sure that your question is complete so I included two versions: have a look:

Explanation:

1] As it is:
`9y^2+16=-24`
`9y^2=-16-24`
`y^2=-40/9`
If you use complex numbers you can introduce the imaaginary unit `i=sqrt(-1)` and get:
`y=+-sqrt(-40/9)`
`y=+-sqrt(-1*40/9)`
`y=+-isqrt(40/9)=+-isqrt(4*10/9)=+-2/3isqrt(10)`

2] How I think it is:
`9y^2+16=-24color(red)(x)`
`9y^2+24y+16=0`
Using the Quadratic Formula:
`y_(1,2)=(-24+-sqrt(576-576))/18=-24/18=-4/3`