1=-3x^2-6x+1

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

1=-3x^2-6x+1

We move all terms to the left:

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

We get rid of parentheses

3x^2+6x-1+1=0

We add all the numbers together, and all the variables

3x^2+6x=0

a = 3; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·3·0
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{-(6)-6}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*3}=\frac{0}{6}
=0
$