(4w+1)(9+w)=0

Solution for (4w+1)(9+w)=0 equation:

(4w+1)(9+w)=0

We add all the numbers together, and all the variables

(4w+1)(w+9)=0

We multiply parentheses ..

(+4w^2+36w+w+9)=0

We get rid of parentheses

4w^2+36w+w+9=0

We add all the numbers together, and all the variables

4w^2+37w+9=0

a = 4; b = 37; c = +9;
Δ = b2-4ac
Δ = 372-4·4·9
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-35}{2*4}=\frac{-72}{8}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+35}{2*4}=\frac{-2}{8}
=-1/4
$