9w^2+1=-9w

Solution for 9w^2+1=-9w equation:

9w^2+1=-9w

We move all terms to the left:

9w^2+1-(-9w)=0

We get rid of parentheses

9w^2+9w+1=0

a = 9; b = 9; c = +1;
Δ = b2-4ac
Δ = 92-4·9·1
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{5}}{2*9}=\frac{-9-3\sqrt{5}}{18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{5}}{2*9}=\frac{-9+3\sqrt{5}}{18}
$