(4w+7)(2+w)=0

Solution for (4w+7)(2+w)=0 equation:

(4w+7)(2+w)=0

We add all the numbers together, and all the variables

(4w+7)(w+2)=0

We multiply parentheses ..

(+4w^2+8w+7w+14)=0

We get rid of parentheses

4w^2+8w+7w+14=0

We add all the numbers together, and all the variables

4w^2+15w+14=0

a = 4; b = 15; c = +14;
Δ = b2-4ac
Δ = 152-4·4·14
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-1}{2*4}=\frac{-16}{8}
=-2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+1}{2*4}=\frac{-14}{8}
=-1+3/4
$