-4x^2+4x+4=-22

Solution for -4x^2+4x+4=-22 equation:

-4x^2+4x+4=-22

We move all terms to the left:

-4x^2+4x+4-(-22)=0

We add all the numbers together, and all the variables

-4x^2+4x+26=0

a = -4; b = 4; c = +26;
Δ = b2-4ac
Δ = 42-4·(-4)·26
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12\sqrt{3}}{2*-4}=\frac{-4-12\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12\sqrt{3}}{2*-4}=\frac{-4+12\sqrt{3}}{-8}
$