1/2z-3/4z=1

Solution for 1/2z-3/4z=1 equation:

1/2z-3/4z=1

We move all terms to the left:

1/2z-3/4z-(1)=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 calculate fractions


4z/8z^2+(-6z)/8z^2-1=0

We multiply all the terms by the denominator


4z+(-6z)-1*8z^2=0

Wy multiply elements

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

We get rid of parentheses

-8z^2+4z-6z=0

We add all the numbers together, and all the variables

-8z^2-2z=0

a = -8; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-8)·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*-8}=\frac{0}{-16}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-8}=\frac{4}{-16}
=-1/4
$