1/4z+1/2z=1/2-11

Solution for 1/4z+1/2z=1/2-11 equation:

1/4z+1/2z=1/2-11

We move all terms to the left:

1/4z+1/2z-(1/2-11)=0


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R



Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We get rid of parentheses

1/4z+1/2z+11-1/2=0

We calculate fractions


8z/32z^2+4z/32z^2+(-4z)/32z^2+11=0

We multiply all the terms by the denominator


8z+4z+(-4z)+11*32z^2=0

We add all the numbers together, and all the variables

12z+(-4z)+11*32z^2=0

Wy multiply elements

352z^2+12z+(-4z)=0

We get rid of parentheses

352z^2+12z-4z=0

We add all the numbers together, and all the variables

352z^2+8z=0

a = 352; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·352·0
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*352}=\frac{-16}{704}
=-1/44
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*352}=\frac{0}{704}
=0
$