11/z-9/2z=1

Solution for 11/z-9/2z=1 equation:

11/z-9/2z=1

We move all terms to the left:

11/z-9/2z-(1)=0


Domain of the equation: z!=0

z∈R



Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We calculate fractions


22z/2z^2+(-9z)/2z^2-1=0

We multiply all the terms by the denominator


22z+(-9z)-1*2z^2=0

Wy multiply elements

-2z^2+22z+(-9z)=0

We get rid of parentheses

-2z^2+22z-9z=0

We add all the numbers together, and all the variables

-2z^2+13z=0

a = -2; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-2)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-2}=\frac{-26}{-4}
=6+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-2}=\frac{0}{-4}
=0
$