w^2-28w-17=0

Solution for w^2-28w-17=0 equation:

w^2-28w-17=0

a = 1; b = -28; c = -17;
Δ = b2-4ac
Δ = -282-4·1·(-17)
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{213}}{2*1}=\frac{28-2\sqrt{213}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{213}}{2*1}=\frac{28+2\sqrt{213}}{2}
$