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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-2(+x^2-2x+6x-12)+1=0

We multiply parentheses

-2x^2+4x-12x+24+1=0

We add all the numbers together, and all the variables

-2x^2-8x+25=0

a = -2; b = -8; c = +25;
Δ = b2-4ac
Δ = -82-4·(-2)·25
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{66}}{2*-2}=\frac{8-2\sqrt{66}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{66}}{2*-2}=\frac{8+2\sqrt{66}}{-4}
$