(6-w)(2w-7)=0

Solution for (6-w)(2w-7)=0 equation:

(6-w)(2w-7)=0

We add all the numbers together, and all the variables

(-1w+6)(2w-7)=0

We multiply parentheses ..

(-2w^2+7w+12w-42)=0

We get rid of parentheses

-2w^2+7w+12w-42=0

We add all the numbers together, and all the variables

-2w^2+19w-42=0

a = -2; b = 19; c = -42;
Δ = b2-4ac
Δ = 192-4·(-2)·(-42)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-5}{2*-2}=\frac{-24}{-4}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+5}{2*-2}=\frac{-14}{-4}
=3+1/2
$