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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+4w^2+28w+3w+21)=0

We get rid of parentheses

4w^2+28w+3w+21=0

We add all the numbers together, and all the variables

4w^2+31w+21=0

a = 4; b = 31; c = +21;
Δ = b2-4ac
Δ = 312-4·4·21
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-25}{2*4}=\frac{-56}{8}
=-7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+25}{2*4}=\frac{-6}{8}
=-3/4
$