9=4w^2+4w

Solution for 9=4w^2+4w equation:

9=4w^2+4w

We move all terms to the left:

9-(4w^2+4w)=0

We get rid of parentheses

-4w^2-4w+9=0

a = -4; b = -4; c = +9;
Δ = b2-4ac
Δ = -42-4·(-4)·9
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{10}}{2*-4}=\frac{4-4\sqrt{10}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{10}}{2*-4}=\frac{4+4\sqrt{10}}{-8}
$