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

Solution for 3-2x-x(x+1)=-3x-6 equation:

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+9=0

a = -1; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-1)·9
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-1}=\frac{6}{-2}
=-3
$