(1+2w)w=55

Solution for (1+2w)w=55 equation:

(1+2w)w=55

We move all terms to the left:

(1+2w)w-(55)=0

We add all the numbers together, and all the variables

(2w+1)w-55=0

We multiply parentheses

2w^2+w-55=0

a = 2; b = 1; c = -55;
Δ = b2-4ac
Δ = 12-4·2·(-55)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-21}{2*2}=\frac{-22}{4}
=-5+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+21}{2*2}=\frac{20}{4}
=5
$