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

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

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

We move all terms to the left:

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


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R


We get rid of parentheses

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

We calculate fractions


4z/32z^2+(-8z)/32z^2+(-4z)/32z^2+5=0

We multiply all the terms by the denominator


4z+(-8z)+(-4z)+5*32z^2=0

Wy multiply elements

160z^2+4z+(-8z)+(-4z)=0

We get rid of parentheses

160z^2+4z-8z-4z=0

We add all the numbers together, and all the variables

160z^2-8z=0

a = 160; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·160·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*160}=\frac{0}{320}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*160}=\frac{16}{320}
=1/20
$