40=(5w-17)w

Solution for 40=(5w-17)w equation:

40=(5w-17)w

We move all terms to the left:

40-((5w-17)w)=0


We calculate terms in parentheses: -((5w-17)w), so:

(5w-17)w

We multiply parentheses

5w^2-17w

Back to the equation:

-(5w^2-17w)


We get rid of parentheses

-5w^2+17w+40=0

a = -5; b = 17; c = +40;
Δ = b2-4ac
Δ = 172-4·(-5)·40
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-33}{2*-5}=\frac{-50}{-10}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+33}{2*-5}=\frac{16}{-10}
=-1+3/5
$