3/4z-1=5/6z

Solution for 3/4z-1=5/6z equation:

3/4z-1=5/6z

We move all terms to the left:

3/4z-1-(5/6z)=0


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R



Domain of the equation: 6z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

3/4z-(+5/6z)-1=0

We get rid of parentheses

3/4z-5/6z-1=0

We calculate fractions


18z/24z^2+(-20z)/24z^2-1=0

We multiply all the terms by the denominator


18z+(-20z)-1*24z^2=0

Wy multiply elements

-24z^2+18z+(-20z)=0

We get rid of parentheses

-24z^2+18z-20z=0

We add all the numbers together, and all the variables

-24z^2-2z=0

a = -24; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-24)·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*-24}=\frac{0}{-48}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-24}=\frac{4}{-48}
=-1/12
$