-4x2+8x+44=16

Solution for -4x2+8x+44=16 equation:

-4x^2+8x+44=16

We move all terms to the left:

-4x^2+8x+44-(16)=0

We add all the numbers together, and all the variables

-4x^2+8x+28=0

a = -4; b = 8; c = +28;
Δ = b2-4ac
Δ = 82-4·(-4)·28
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16\sqrt{2}}{2*-4}=\frac{-8-16\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16\sqrt{2}}{2*-4}=\frac{-8+16\sqrt{2}}{-8}
$