1/6912z+18)=2z+-3

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Solution for 1/6912z+18)=2z+-3 equation:



1/6912z+18)=2z+-3
We move all terms to the left:
1/6912z+18)-(2z+-3)=0
Domain of the equation: 6912z!=0
z!=0/6912
z!=0
z∈R
We add all the numbers together, and all the variables
1/6912z+18)-(2z-3)=0
We add all the numbers together, and all the variables
1/6912z+18)-(2z=0
We multiply all the terms by the denominator
-2z*6912z+1+18=0
We add all the numbers together, and all the variables
-2z*6912z+19=0
Wy multiply elements
-13824z^2+19=0
a = -13824; b = 0; c = +19;
Δ = b2-4ac
Δ = 02-4·(-13824)·19
Δ = 1050624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{1050624}=\sqrt{9216*114}=\sqrt{9216}*\sqrt{114}=96\sqrt{114}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96\sqrt{114}}{2*-13824}=\frac{0-96\sqrt{114}}{-27648} =-\frac{96\sqrt{114}}{-27648} =-\frac{\sqrt{114}}{-288} $
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96\sqrt{114}}{2*-13824}=\frac{0+96\sqrt{114}}{-27648} =\frac{96\sqrt{114}}{-27648} =\frac{\sqrt{114}}{-288} $

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