-3x(2x+2)=1

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

-3x(2x+2)=1

We move all terms to the left:

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

We multiply parentheses

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

a = -6; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·(-6)·(-1)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3}}{2*-6}=\frac{6-2\sqrt{3}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3}}{2*-6}=\frac{6+2\sqrt{3}}{-12}
$