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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-2x(x+3)-4=0

We multiply parentheses

-2x^2-6x-4=0

a = -2; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·(-2)·(-4)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*-2}=\frac{4}{-4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*-2}=\frac{8}{-4}
=-2
$