0=11x^2+16x-1

Solution for 0=11x^2+16x-1 equation:

0=11x^2+16x-1

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -11; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·(-11)·1
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*-11}=\frac{16-10\sqrt{3}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+10\sqrt{3}}{2*-11}=\frac{16+10\sqrt{3}}{-22}
$