/9z+1=9z-1

Solution for /9z+1=9z-1 equation:

/9z+1=9z-1

We move all terms to the left:

/9z+1-(9z-1)=0


Domain of the equation: 9z!=0

z!=0/9

z!=0

z∈R


We get rid of parentheses

/9z-9z+1+1=0

We multiply all the terms by the denominator


-9z*9z+1*9z+1*9z+=0

We add all the numbers together, and all the variables

-9z*9z+1*9z+1*9z=0

Wy multiply elements

-81z^2+9z+9z=0

We add all the numbers together, and all the variables

-81z^2+18z=0

a = -81; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-81)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-81}=\frac{-36}{-162}
=2/9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-81}=\frac{0}{-162}
=0
$