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

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}
$