w(2w+9)+1=0

Solution for w(2w+9)+1=0 equation:

w(2w+9)+1=0

We multiply parentheses

2w^2+9w+1=0

a = 2; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·2·1
Δ = 73
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{73}}{2*2}=\frac{-9-\sqrt{73}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{73}}{2*2}=\frac{-9+\sqrt{73}}{4}
$