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

Solution for (1+w)(5w-7)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+5w^2-7w+5w-7)=0

We get rid of parentheses

5w^2-7w+5w-7=0

We add all the numbers together, and all the variables

5w^2-2w-7=0

a = 5; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·5·(-7)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12}{2*5}=\frac{-10}{10}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*5}=\frac{14}{10}
=1+2/5
$