(6-w)(2w-1)=0

Solution for (6-w)(2w-1)=0 equation:

(6-w)(2w-1)=0

We add all the numbers together, and all the variables

(-1w+6)(2w-1)=0

We multiply parentheses ..

(-2w^2+w+12w-6)=0

We get rid of parentheses

-2w^2+w+12w-6=0

We add all the numbers together, and all the variables

-2w^2+13w-6=0

a = -2; b = 13; c = -6;
Δ = b2-4ac
Δ = 132-4·(-2)·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-11}{2*-2}=\frac{-24}{-4}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+11}{2*-2}=\frac{-2}{-4}
=1/2
$