z-3/z+5=1

Solution for z-3/z+5=1 equation:

z-3/z+5=1

We move all terms to the left:

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


Domain of the equation: z!=0

z∈R


We add all the numbers together, and all the variables

z-3/z+4=0

We multiply all the terms by the denominator


z*z+4*z-3=0

We add all the numbers together, and all the variables

4z+z*z-3=0

Wy multiply elements

z^2+4z-3=0

a = 1; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·1·(-3)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{7}}{2*1}=\frac{-4-2\sqrt{7}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{7}}{2*1}=\frac{-4+2\sqrt{7}}{2}
$