35=(w-2)(w)

Solution for 35=(w-2)(w) equation:

35=(w-2)(w)

We move all terms to the left:

35-((w-2)(w))=0


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

(w-2)w

We multiply parentheses

w^2-2w

Back to the equation:

-(w^2-2w)


We get rid of parentheses

-w^2+2w+35=0

We add all the numbers together, and all the variables

-1w^2+2w+35=0

a = -1; b = 2; c = +35;
Δ = b2-4ac
Δ = 22-4·(-1)·35
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-12}{2*-1}=\frac{-14}{-2}
=+7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+12}{2*-1}=\frac{10}{-2}
=-5
$