200=0.1w^2+2.155w+19.985

Solution for 200=0.1w^2+2.155w+19.985 equation:

200=0.1w^2+2.155w+19.985

We move all terms to the left:

200-(0.1w^2+2.155w+19.985)=0

We get rid of parentheses

-0.1w^2-2.155w-19.985+200=0

We add all the numbers together, and all the variables

-0.1w^2-2.155w+180.015=0

a = -0.1; b = -2.155; c = +180.015;
Δ = b2-4ac
Δ = -2.1552-4·(-0.1)·180.015
Δ = 76.650025
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{-(-2.155)-\sqrt{76.650025}}{2*-0.1}=\frac{2.155-\sqrt{76.650025}}{-0.2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.155)+\sqrt{76.650025}}{2*-0.1}=\frac{2.155+\sqrt{76.650025}}{-0.2}
$