3x+6=-12+x2-4

Solution for 3x+6=-12+x2-4 equation:

3x+6=-12+x2-4

We move all terms to the left:

3x+6-(-12+x2-4)=0

We add all the numbers together, and all the variables

-(+x^2-12-4)+3x+6=0

We get rid of parentheses

-x^2+3x+12+4+6=0

We add all the numbers together, and all the variables

-1x^2+3x+22=0

a = -1; b = 3; c = +22;
Δ = b2-4ac
Δ = 32-4·(-1)·22
Δ = 97
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{-(3)-\sqrt{97}}{2*-1}=\frac{-3-\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{97}}{2*-1}=\frac{-3+\sqrt{97}}{-2}
$