(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

(w+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
$