(7-w)(5w+8)=0

Solution for (7-w)(5w+8)=0 equation:

(7-w)(5w+8)=0

We add all the numbers together, and all the variables

(-1w+7)(5w+8)=0

We multiply parentheses ..

(-5w^2-8w+35w+56)=0

We get rid of parentheses

-5w^2-8w+35w+56=0

We add all the numbers together, and all the variables

-5w^2+27w+56=0

a = -5; b = 27; c = +56;
Δ = b2-4ac
Δ = 272-4·(-5)·56
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-43}{2*-5}=\frac{-70}{-10}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+43}{2*-5}=\frac{16}{-10}
=-1+3/5
$