-b^2-11b+17=0

Solution for -b^2-11b+17=0 equation:

-b^2-11b+17=0

We add all the numbers together, and all the variables

-1b^2-11b+17=0

a = -1; b = -11; c = +17;
Δ = b2-4ac
Δ = -112-4·(-1)·17
Δ = 189
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{21}}{2*-1}=\frac{11-3\sqrt{21}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{21}}{2*-1}=\frac{11+3\sqrt{21}}{-2}
$