-16x^2-8x+20=1

Solution for -16x^2-8x+20=1 equation:

-16x^2-8x+20=1

We move all terms to the left:

-16x^2-8x+20-(1)=0

We add all the numbers together, and all the variables

-16x^2-8x+19=0

a = -16; b = -8; c = +19;
Δ = b2-4ac
Δ = -82-4·(-16)·19
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16\sqrt{5}}{2*-16}=\frac{8-16\sqrt{5}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{5}}{2*-16}=\frac{8+16\sqrt{5}}{-32}
$