45=(2w+1)w

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

45=(2w+1)w

We move all terms to the left:

45-((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+45=0

We add all the numbers together, and all the variables

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

a = -2; b = -1; c = +45;
Δ = b2-4ac
Δ = -12-4·(-2)·45
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*-2}=\frac{20}{-4}
=-5
$