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

Solution for (6+w)(3w-1)=0 equation:

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

We add all the numbers together, and all the variables

(w+6)(3w-1)=0

We multiply parentheses ..

(+3w^2-1w+18w-6)=0

We get rid of parentheses

3w^2-1w+18w-6=0

We add all the numbers together, and all the variables

3w^2+17w-6=0

a = 3; b = 17; c = -6;
Δ = b2-4ac
Δ = 172-4·3·(-6)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-19}{2*3}=\frac{-36}{6}
=-6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+19}{2*3}=\frac{2}{6}
=1/3
$