w2+9w+1=0

Solution for w2+9w+1=0 equation:

w2+9w+1=0

We add all the numbers together, and all the variables

w^2+9w+1=0

a = 1; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·1·1
Δ = 77
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{77}}{2*1}=\frac{-9-\sqrt{77}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{77}}{2*1}=\frac{-9+\sqrt{77}}{2}
$