-2x^2-4x=1

Solution for -2x^2-4x=1 equation:

-2x^2-4x=1

We move all terms to the left:

-2x^2-4x-(1)=0

a = -2; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·(-2)·(-1)
Δ = 8
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:

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