-2x-x^2=3x+6

Solution for -2x-x^2=3x+6 equation:

-2x-x^2=3x+6

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x^2-2x-(3x+6)=0

We get rid of parentheses

-1x^2-2x-3x-6=0

We add all the numbers together, and all the variables

-1x^2-5x-6=0

a = -1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·(-1)·(-6)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*-1}=\frac{4}{-2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*-1}=\frac{6}{-2}
=-3
$