(3w+7)(4-w)=0

Solution for (3w+7)(4-w)=0 equation:

(3w+7)(4-w)=0

We add all the numbers together, and all the variables

(3w+7)(-1w+4)=0

We multiply parentheses ..

(-3w^2+12w-7w+28)=0

We get rid of parentheses

-3w^2+12w-7w+28=0

We add all the numbers together, and all the variables

-3w^2+5w+28=0

a = -3; b = 5; c = +28;
Δ = b2-4ac
Δ = 52-4·(-3)·28
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{-(5)-19}{2*-3}=\frac{-24}{-6}
=+4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*-3}=\frac{14}{-6}
=-2+1/3
$