1/2(z)+(-1)=5-z

Solution for 1/2(z)+(-1)=5-z equation:

1/2(z)+(-1)=5-z

We move all terms to the left:

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


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1z*2z-5*2z-1*2z+1=0

Wy multiply elements

2z^2-10z-2z+1=0

We add all the numbers together, and all the variables

2z^2-12z+1=0

a = 2; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·2·1
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{34}}{2*2}=\frac{12-2\sqrt{34}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{34}}{2*2}=\frac{12+2\sqrt{34}}{4}
$