1/2z+2=1/4z+6

Solution for 1/2z+2=1/4z+6 equation:

1/2z+2=1/4z+6

We move all terms to the left:

1/2z+2-(1/4z+6)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 4z+6)!=0

z∈R


We get rid of parentheses

1/2z-1/4z-6+2=0

We calculate fractions


4z/8z^2+(-2z)/8z^2-6+2=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-32z^2+4z+(-2z)=0

We get rid of parentheses

-32z^2+4z-2z=0

We add all the numbers together, and all the variables

-32z^2+2z=0

a = -32; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-32)·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*-32}=\frac{-4}{-64}
=1/16
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-32}=\frac{0}{-64}
=0
$