(2w+5)(w-8)=8

Solution for (2w+5)(w-8)=8 equation:

(2w+5)(w-8)=8

We move all terms to the left:

(2w+5)(w-8)-(8)=0

We multiply parentheses ..

(+2w^2-16w+5w-40)-8=0

We get rid of parentheses

2w^2-16w+5w-40-8=0

We add all the numbers together, and all the variables

2w^2-11w-48=0

a = 2; b = -11; c = -48;
Δ = b2-4ac
Δ = -112-4·2·(-48)
Δ = 505
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{505}}{2*2}=\frac{11-\sqrt{505}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{505}}{2*2}=\frac{11+\sqrt{505}}{4}
$