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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+2w^2+7w+14w+49)=0

We get rid of parentheses

2w^2+7w+14w+49=0

We add all the numbers together, and all the variables

2w^2+21w+49=0

a = 2; b = 21; c = +49;
Δ = b2-4ac
Δ = 212-4·2·49
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-7}{2*2}=\frac{-28}{4}
=-7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+7}{2*2}=\frac{-14}{4}
=-3+1/2
$