w^2=19w-20

Solution for w^2=19w-20 equation:

w^2=19w-20

We move all terms to the left:

w^2-(19w-20)=0

We get rid of parentheses

w^2-19w+20=0

a = 1; b = -19; c = +20;
Δ = b2-4ac
Δ = -192-4·1·20
Δ = 281
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{-(-19)-\sqrt{281}}{2*1}=\frac{19-\sqrt{281}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{281}}{2*1}=\frac{19+\sqrt{281}}{2}
$