w^2+18w+17=0

Solution for w^2+18w+17=0 equation:

w^2+18w+17=0

a = 1; b = 18; c = +17;
Δ = b2-4ac
Δ = 182-4·1·17
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-16}{2*1}=\frac{-34}{2}
=-17
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+16}{2*1}=\frac{-2}{2}
=-1
$