-x^2-16x+11=0

Solution for -x^2-16x+11=0 equation:

-x^2-16x+11=0

We add all the numbers together, and all the variables

-1x^2-16x+11=0

a = -1; b = -16; c = +11;
Δ = b2-4ac
Δ = -162-4·(-1)·11
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-10\sqrt{3}}{2*-1}=\frac{16-10\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+10\sqrt{3}}{2*-1}=\frac{16+10\sqrt{3}}{-2}
$