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

Solution for (8-w)(5w+1)=) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5w^2-1w+40w+8)=0

We get rid of parentheses

-5w^2-1w+40w+8=0

We add all the numbers together, and all the variables

-5w^2+39w+8=0

a = -5; b = 39; c = +8;
Δ = b2-4ac
Δ = 392-4·(-5)·8
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-41}{2*-5}=\frac{-80}{-10}
=+8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+41}{2*-5}=\frac{2}{-10}
=-1/5
$