b^2+8b-77=-9

Solution for b^2+8b-77=-9 equation:

b^2+8b-77=-9

We move all terms to the left:

b^2+8b-77-(-9)=0

We add all the numbers together, and all the variables

b^2+8b-68=0

a = 1; b = 8; c = -68;
Δ = b2-4ac
Δ = 82-4·1·(-68)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{21}}{2*1}=\frac{-8-4\sqrt{21}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{21}}{2*1}=\frac{-8+4\sqrt{21}}{2}
$