210=2w^2+18w+81

Solution for 210=2w^2+18w+81 equation:

210=2w^2+18w+81

We move all terms to the left:

210-(2w^2+18w+81)=0

We get rid of parentheses

-2w^2-18w-81+210=0

We add all the numbers together, and all the variables

-2w^2-18w+129=0

a = -2; b = -18; c = +129;
Δ = b2-4ac
Δ = -182-4·(-2)·129
Δ = 1356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1356}=\sqrt{4*339}=\sqrt{4}*\sqrt{339}=2\sqrt{339}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{339}}{2*-2}=\frac{18-2\sqrt{339}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{339}}{2*-2}=\frac{18+2\sqrt{339}}{-4}
$