w^2=19w

Solution for w^2=19w equation:

w^2=19w

We move all terms to the left:

w^2-(19w)=0

a = 1; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·1·0
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{-(-19)-19}{2*1}=\frac{0}{2}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*1}=\frac{38}{2}
=19
$