z+1=(1/2z)+4

Solution for z+1=(1/2z)+4 equation:

z+1=(1/2z)+4

We move all terms to the left:

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


Domain of the equation: 2z)+4)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


z*2z)+4)-((+1*2z)+4)+1=0

Wy multiply elements

2z^2+2z=0

a = 2; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·2·0
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*2}=\frac{-4}{4}
=-1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*2}=\frac{0}{4}
=0
$