40=w(2w-4)

Solution for 40=w(2w-4) equation:

40=w(2w-4)

We move all terms to the left:

40-(w(2w-4))=0


We calculate terms in parentheses: -(w(2w-4)), so:

w(2w-4)

We multiply parentheses

2w^2-4w

Back to the equation:

-(2w^2-4w)


We get rid of parentheses

-2w^2+4w+40=0

a = -2; b = 4; c = +40;
Δ = b2-4ac
Δ = 42-4·(-2)·40
Δ = 336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{21}}{2*-2}=\frac{-4-4\sqrt{21}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{21}}{2*-2}=\frac{-4+4\sqrt{21}}{-4}
$