(2w-1)w=45

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

(2w-1)w=45

We move all terms to the left:

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

We multiply parentheses

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
$