(7-w)(3w-2)=0

Solution for (7-w)(3w-2)=0 equation:

(7-w)(3w-2)=0

We add all the numbers together, and all the variables

(-1w+7)(3w-2)=0

We multiply parentheses ..

(-3w^2+2w+21w-14)=0

We get rid of parentheses

-3w^2+2w+21w-14=0

We add all the numbers together, and all the variables

-3w^2+23w-14=0

a = -3; b = 23; c = -14;
Δ = b2-4ac
Δ = 232-4·(-3)·(-14)
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{-(23)-19}{2*-3}=\frac{-42}{-6}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+19}{2*-3}=\frac{-4}{-6}
=2/3
$