w*w/2=81

Solution for w*w/2=81 equation:

w*w/2=81

We move all terms to the left:

w*w/2-(81)=0

We multiply all the terms by the denominator


w*w-81*2=0

We add all the numbers together, and all the variables

w*w-162=0

Wy multiply elements

w^2-162=0

a = 1; b = 0; c = -162;
Δ = b2-4ac
Δ = 02-4·1·(-162)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*1}=\frac{0-18\sqrt{2}}{2}
=-\frac{18\sqrt{2}}{2}
=-9\sqrt{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*1}=\frac{0+18\sqrt{2}}{2}
=\frac{18\sqrt{2}}{2}
=9\sqrt{2}
$