-4x2+4x=-2

Solution for -4x2+4x=-2 equation:

-4x^2+4x=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-4x^2+4x+2=0

a = -4; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·(-4)·2
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{3}}{2*-4}=\frac{-4-4\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{3}}{2*-4}=\frac{-4+4\sqrt{3}}{-8}
$