(2w-5)(w)=85.9

Solution for (2w-5)(w)=85.9 equation:

(2w-5)(w)=85.9

We move all terms to the left:

(2w-5)(w)-(85.9)=0

We add all the numbers together, and all the variables

(2w-5)w-85.9=0

We multiply parentheses

2w^2-5w-85.9=0

a = 2; b = -5; c = -85.9;
Δ = b2-4ac
Δ = -52-4·2·(-85.9)
Δ = 712.2
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{-(-5)-\sqrt{712.2}}{2*2}=\frac{5-\sqrt{712.2}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{712.2}}{2*2}=\frac{5+\sqrt{712.2}}{4}
$