w^2-8w-31=0

Solution for w^2-8w-31=0 equation:

w^2-8w-31=0

a = 1; b = -8; c = -31;
Δ = b2-4ac
Δ = -82-4·1·(-31)
Δ = 188
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{47}}{2*1}=\frac{8-2\sqrt{47}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{47}}{2*1}=\frac{8+2\sqrt{47}}{2}
$