-4x^2-16x+19=-17

Solution for -4x^2-16x+19=-17 equation:

-4x^2-16x+19=-17

We move all terms to the left:

-4x^2-16x+19-(-17)=0

We add all the numbers together, and all the variables

-4x^2-16x+36=0

a = -4; b = -16; c = +36;
Δ = b2-4ac
Δ = -162-4·(-4)·36
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{13}}{2*-4}=\frac{16-8\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{13}}{2*-4}=\frac{16+8\sqrt{13}}{-8}
$