1/23*w=18

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Solution for 1/23*w=18 equation:



1/23*w=18
We move all terms to the left:
1/23*w-(18)=0
Domain of the equation: 23*w!=0
w!=0/1
w!=0
w∈R
We multiply all the terms by the denominator
-18*23*w+1=0
Wy multiply elements
-414w*w+1=0
Wy multiply elements
-414w^2+1=0
a = -414; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-414)·1
Δ = 1656
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:
$\sqrt{\Delta}=\sqrt{1656}=\sqrt{36*46}=\sqrt{36}*\sqrt{46}=6\sqrt{46}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{46}}{2*-414}=\frac{0-6\sqrt{46}}{-828} =-\frac{6\sqrt{46}}{-828} =-\frac{\sqrt{46}}{-138} $
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{46}}{2*-414}=\frac{0+6\sqrt{46}}{-828} =\frac{6\sqrt{46}}{-828} =\frac{\sqrt{46}}{-138} $

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