X+4=x^2-4

Solution for X+4=x^2-4 equation:

X+4=X^2-4

We move all terms to the left:

X+4-(X^2-4)=0

We get rid of parentheses

-X^2+X+4+4=0

We add all the numbers together, and all the variables

-1X^2+X+8=0

a = -1; b = 1; c = +8;
Δ = b2-4ac
Δ = 12-4·(-1)·8
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{33}}{2*-1}=\frac{-1-\sqrt{33}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*-1}=\frac{-1+\sqrt{33}}{-2}
$