b^2-6b-13=0

Solution for b^2-6b-13=0 equation:

b^2-6b-13=0

a = 1; b = -6; c = -13;
Δ = b2-4ac
Δ = -62-4·1·(-13)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{22}}{2*1}=\frac{6-2\sqrt{22}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{22}}{2*1}=\frac{6+2\sqrt{22}}{2}
$