210=(2w+1)*w

Solution for 210=(2w+1)*w equation:

210=(2w+1)*w

We move all terms to the left:

210-((2w+1)*w)=0


We calculate terms in parentheses: -((2w+1)*w), so:

(2w+1)*w

We multiply parentheses

2w^2+w

Back to the equation:

-(2w^2+w)


We get rid of parentheses

-2w^2-w+210=0

We add all the numbers together, and all the variables

-2w^2-1w+210=0

a = -2; b = -1; c = +210;
Δ = b2-4ac
Δ = -12-4·(-2)·210
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-41}{2*-2}=\frac{-40}{-4}
=+10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+41}{2*-2}=\frac{42}{-4}
=-10+1/2
$