100=w(2w-1)

Solution for 100=w(2w-1) equation:

100=w(2w-1)

We move all terms to the left:

100-(w(2w-1))=0


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

w(2w-1)

We multiply parentheses

2w^2-1w

Back to the equation:

-(2w^2-1w)


We get rid of parentheses

-2w^2+1w+100=0

We add all the numbers together, and all the variables

-2w^2+w+100=0

a = -2; b = 1; c = +100;
Δ = b2-4ac
Δ = 12-4·(-2)·100
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{89}}{2*-2}=\frac{-1-3\sqrt{89}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{89}}{2*-2}=\frac{-1+3\sqrt{89}}{-4}
$