b^2-12b-11=0

Solution for b^2-12b-11=0 equation:

b^2-12b-11=0

a = 1; b = -12; c = -11;
Δ = b2-4ac
Δ = -122-4·1·(-11)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{47}}{2*1}=\frac{12-2\sqrt{47}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{47}}{2*1}=\frac{12+2\sqrt{47}}{2}
$