(9+w)(3w-1)=0

Solution for (9+w)(3w-1)=0 equation:

(9+w)(3w-1)=0

We add all the numbers together, and all the variables

(w+9)(3w-1)=0

We multiply parentheses ..

(+3w^2-1w+27w-9)=0

We get rid of parentheses

3w^2-1w+27w-9=0

We add all the numbers together, and all the variables

3w^2+26w-9=0

a = 3; b = 26; c = -9;
Δ = b2-4ac
Δ = 262-4·3·(-9)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-28}{2*3}=\frac{-54}{6}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+28}{2*3}=\frac{2}{6}
=1/3
$