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

Oct 3, 2016

There are no Real solutions (as demonstrated below).
If Complex solutions are permitted $x = i \sqrt{5} \mathmr{and} - i \sqrt{5}$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} - 4 = - 3 {x}^{2} - 24$

Get all terms with the variable $x$ on the left side
by adding $3 {x}^{2}$ to both sides:
$\textcolor{w h i t e}{\text{XXX}} 4 {x}^{2} - 4 = - 24$

Get all the constant terms on the right side
by adding $4$ to both sides:
$\textcolor{w h i t e}{\text{XXX}} 4 {x}^{2} = - 20$

Divide both sides by $4$
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} = - 5$

Take the square root of both sides
$\textcolor{w h i t e}{\text{XXX}} x = \pm \sqrt{- 5}$

...as noted in the answer there are no Real solutions;
but among Complex numbers $\sqrt{- 1} = i$ and $\sqrt{- 5} = i \sqrt{5}$