Z/9z-15=9-3z

Solution for Z/9z-15=9-3z equation:

/9Z-15=9-3Z

We move all terms to the left:

/9Z-15-(9-3Z)=0


Domain of the equation: 9Z!=0

Z!=0/9

Z!=0

Z∈R


We add all the numbers together, and all the variables

/9Z-(-3Z+9)-15=0

We get rid of parentheses

/9Z+3Z-9-15=0

We multiply all the terms by the denominator


3Z*9Z-9*9Z-15*9Z+=0

We add all the numbers together, and all the variables

3Z*9Z-9*9Z-15*9Z=0

Wy multiply elements

27Z^2-81Z-135Z=0

We add all the numbers together, and all the variables

27Z^2-216Z=0

a = 27; b = -216; c = 0;
Δ = b2-4ac
Δ = -2162-4·27·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-216}{2*27}=\frac{0}{54}
=0
$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+216}{2*27}=\frac{432}{54}
=8
$