w^2-16w-47=0

Solution for w^2-16w-47=0 equation:

w^2-16w-47=0

a = 1; b = -16; c = -47;
Δ = b2-4ac
Δ = -162-4·1·(-47)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{111}}{2*1}=\frac{16-2\sqrt{111}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{111}}{2*1}=\frac{16+2\sqrt{111}}{2}
$