0=4x^2+4x-16

Solution for 0=4x^2+4x-16 equation:

0=4x^2+4x-16

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -4; b = -4; c = +16;
Δ = b2-4ac
Δ = -42-4·(-4)·16
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{17}}{2*-4}=\frac{4-4\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{17}}{2*-4}=\frac{4+4\sqrt{17}}{-8}
$