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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+4w^2-1w+36w-9)=0

We get rid of parentheses

4w^2-1w+36w-9=0

We add all the numbers together, and all the variables

4w^2+35w-9=0

a = 4; b = 35; c = -9;
Δ = b2-4ac
Δ = 352-4·4·(-9)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-37}{2*4}=\frac{-72}{8}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+37}{2*4}=\frac{2}{8}
=1/4
$