4w^2+22w+9=0

Solution for 4w^2+22w+9=0 equation:

4w^2+22w+9=0

a = 4; b = 22; c = +9;
Δ = b2-4ac
Δ = 222-4·4·9
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{85}}{2*4}=\frac{-22-2\sqrt{85}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{85}}{2*4}=\frac{-22+2\sqrt{85}}{8}
$