5z/2z+8-1/z+4=1

Solution for 5z/2z+8-1/z+4=1 equation:

5z/2z+8-1/z+4=1

We move all terms to the left:

5z/2z+8-1/z+4-(1)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: z!=0

z∈R


We add all the numbers together, and all the variables

5z/2z-1/z+11=0

We calculate fractions


5z^2/2z^2+(-2z)/2z^2+11=0

We multiply all the terms by the denominator


5z^2+(-2z)+11*2z^2=0

Wy multiply elements

5z^2+22z^2+(-2z)=0

We get rid of parentheses

5z^2+22z^2-2z=0

We add all the numbers together, and all the variables

27z^2-2z=0

a = 27; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·27·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*27}=\frac{0}{54}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*27}=\frac{4}{54}
=2/27
$