420=w(2w-2)

Solution for 420=w(2w-2) equation:

420=w(2w-2)

We move all terms to the left:

420-(w(2w-2))=0


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

w(2w-2)

We multiply parentheses

2w^2-2w

Back to the equation:

-(2w^2-2w)


We get rid of parentheses

-2w^2+2w+420=0

a = -2; b = 2; c = +420;
Δ = b2-4ac
Δ = 22-4·(-2)·420
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-58}{2*-2}=\frac{-60}{-4}
=+15
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+58}{2*-2}=\frac{56}{-4}
=-14
$