(5w-4)(7+w)=0

Solution for (5w-4)(7+w)=0 equation:

(5w-4)(7+w)=0

We add all the numbers together, and all the variables

(5w-4)(w+7)=0

We multiply parentheses ..

(+5w^2+35w-4w-28)=0

We get rid of parentheses

5w^2+35w-4w-28=0

We add all the numbers together, and all the variables

5w^2+31w-28=0

a = 5; b = 31; c = -28;
Δ = b2-4ac
Δ = 312-4·5·(-28)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-39}{2*5}=\frac{-70}{10}
=-7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+39}{2*5}=\frac{8}{10}
=4/5
$