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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

-2x^2-6x-x-6=0

We add all the numbers together, and all the variables

-2x^2-7x-6=0

a = -2; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·(-2)·(-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{-(-7)-1}{2*-2}=\frac{6}{-4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*-2}=\frac{8}{-4}
=-2
$