Question

How do you solve `x^2-4=-3x^2-24`?

Answer 1

There are no Real solutions (as demonstrated below).
If Complex solutions are permitted `x=isqrt(5) or -isqrt(5)`

Explanation:

Given
`color(white)("XXX")x^2-4=-3x^2-24`

Get all terms with the variable `x` on the left side
by adding `3x^2` to both sides:
`color(white)("XXX")4x^2-4=-24`

Get all the constant terms on the right side
by adding `4` to both sides:
`color(white)("XXX")4x^2=-20`

Divide both sides by `4`
`color(white)("XXX")x^2=-5`

Take the square root of both sides
`color(white)("XXX")x=+-sqrt(-5)`

...as noted in the answer there are no Real solutions;
but among Complex numbers `sqrt(-1)=i` and `sqrt(-5)=isqrt(5)`