w*w/2=81

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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} $

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