19=w2-6w+3

Solution for 19=w2-6w+3 equation:

19=w2-6w+3

We move all terms to the left:

19-(w2-6w+3)=0

We add all the numbers together, and all the variables

-(+w^2-6w+3)+19=0

We get rid of parentheses

-w^2+6w-3+19=0

We add all the numbers together, and all the variables

-1w^2+6w+16=0

a = -1; b = 6; c = +16;
Δ = b2-4ac
Δ = 62-4·(-1)·16
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*-1}=\frac{-16}{-2}
=+8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*-1}=\frac{4}{-2}
=-2
$