200=72+2w^2

Solution for 200=72+2w^2 equation:

200=72+2w^2

We move all terms to the left:

200-(72+2w^2)=0

We get rid of parentheses

-2w^2-72+200=0

We add all the numbers together, and all the variables

-2w^2+128=0

a = -2; b = 0; c = +128;
Δ = b2-4ac
Δ = 02-4·(-2)·128
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*-2}=\frac{-32}{-4}
=+8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*-2}=\frac{32}{-4}
=-8
$