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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+4w^2+7w+16w+28)=0

We get rid of parentheses

4w^2+7w+16w+28=0

We add all the numbers together, and all the variables

4w^2+23w+28=0

a = 4; b = 23; c = +28;
Δ = b2-4ac
Δ = 232-4·4·28
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-9}{2*4}=\frac{-32}{8}
=-4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+9}{2*4}=\frac{-14}{8}
=-1+3/4
$