9/8z=13z=

Solution for 9/8z=13z= equation:

9/8z=13z=

We move all terms to the left:

9/8z-(13z)=0


Domain of the equation: 8z!=0

z!=0/8

z!=0

z∈R


We add all the numbers together, and all the variables

-13z+9/8z=0

We multiply all the terms by the denominator


-13z*8z+9=0

Wy multiply elements

-104z^2+9=0

a = -104; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-104)·9
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{26}}{2*-104}=\frac{0-12\sqrt{26}}{-208}
=-\frac{12\sqrt{26}}{-208}
=-\frac{3\sqrt{26}}{-52}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{26}}{2*-104}=\frac{0+12\sqrt{26}}{-208}
=\frac{12\sqrt{26}}{-208}
=\frac{3\sqrt{26}}{-52}
$