b^2-16b-14=-8

Solution for b^2-16b-14=-8 equation:

b^2-16b-14=-8

We move all terms to the left:

b^2-16b-14-(-8)=0

We add all the numbers together, and all the variables

b^2-16b-6=0

a = 1; b = -16; c = -6;
Δ = b2-4ac
Δ = -162-4·1·(-6)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{70}}{2*1}=\frac{16-2\sqrt{70}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{70}}{2*1}=\frac{16+2\sqrt{70}}{2}
$