(z-5)/(z-3)=z

Solution for (z-5)/(z-3)=z equation:

(z-5)/(z-3)=z

We move all terms to the left:

(z-5)/(z-3)-(z)=0


Domain of the equation: (z-3)!=0

We move all terms containing z to the left, all other terms to the right

z!=3

z∈R


We add all the numbers together, and all the variables

-1z+(z-5)/(z-3)=0

We multiply all the terms by the denominator


-1z*(z-3)+(z-5)=0

We multiply parentheses

-z^2+3z+(z-5)=0

We get rid of parentheses

-z^2+3z+z-5=0

We add all the numbers together, and all the variables

-1z^2+4z-5=0

a = -1; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·(-1)·(-5)
Δ = -4
Delta is less than zero, so there is no solution for the equation