w^2+81=18w^2

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

w^2+81=18w^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-17w^2+81=0

a = -17; b = 0; c = +81;
Δ = b2-4ac
Δ = 02-4·(-17)·81
Δ = 5508
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:

$\sqrt{\Delta}=\sqrt{5508}=\sqrt{324*17}=\sqrt{324}*\sqrt{17}=18\sqrt{17}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{17}}{2*-17}=\frac{0-18\sqrt{17}}{-34}
=-\frac{18\sqrt{17}}{-34}
=-\frac{9\sqrt{17}}{-17}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{17}}{2*-17}=\frac{0+18\sqrt{17}}{-34}
=\frac{18\sqrt{17}}{-34}
=\frac{9\sqrt{17}}{-17}
$