(2w+1)w=45^2

Solution for (2w+1)w=45^2 equation:

(2w+1)w=45^2

We move all terms to the left:

(2w+1)w-(45^2)=0

We add all the numbers together, and all the variables

(2w+1)w-2025=0

We multiply parentheses

2w^2+w-2025=0

a = 2; b = 1; c = -2025;
Δ = b2-4ac
Δ = 12-4·2·(-2025)
Δ = 16201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{16201}}{2*2}=\frac{-1-\sqrt{16201}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{16201}}{2*2}=\frac{-1+\sqrt{16201}}{4}
$