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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-3w^2+7w+9w-21)=0

We get rid of parentheses

-3w^2+7w+9w-21=0

We add all the numbers together, and all the variables

-3w^2+16w-21=0

a = -3; b = 16; c = -21;
Δ = b2-4ac
Δ = 162-4·(-3)·(-21)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2}{2*-3}=\frac{-18}{-6}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2}{2*-3}=\frac{-14}{-6}
=2+1/3
$