w^2-22w+119=0

Solution for w^2-22w+119=0 equation:

w^2-22w+119=0

a = 1; b = -22; c = +119;
Δ = b2-4ac
Δ = -222-4·1·119
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{2}}{2*1}=\frac{22-2\sqrt{2}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{2}}{2*1}=\frac{22+2\sqrt{2}}{2}
$