-4x^2-16x+16=-32

Solution for -4x^2-16x+16=-32 equation:

-4x^2-16x+16=-32

We move all terms to the left:

-4x^2-16x+16-(-32)=0

We add all the numbers together, and all the variables

-4x^2-16x+48=0

a = -4; b = -16; c = +48;
Δ = b2-4ac
Δ = -162-4·(-4)·48
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-32}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+32}{2*-4}=\frac{48}{-8}
=-6
$